Cluster · Trigonometric Identities and Equations

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Clusters / #1156
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Trigonometric Identities and Expressions
Questions
832
Questions in this cluster
827 total
Question Category Subtype Difficulty

Select the INCORRECT formula from the following options

pipeline-451392
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If 4sin2θ = 3(1 + cosθ ), 0° < θ < 90° Then what is the value of 15tanθ + \(\frac{4 }{√15}\)sinθ  + 2secθ ?

pipeline-668712
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Find the value of (1 + cotA - cosecA) (1 + tanA + secA)-3(sin²A + cos²A)

pipeline-665988
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If sin\(\theta=\frac{2xy}{x^2+y^2}\), then the value of tan\(\theta\) is:

pipeline-668719
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If 12sin² A + 2cos² A = 7. where 0 < A < 180°. Then cot A is:

pipeline-670605
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(1 - cos2A) sec2A is equal to:

pipeline-668694
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If cot A = 7, then the value of \(\frac{5cosA+4sinA}{cos^3A+7sin^3A+6sinA}\)is:

pipeline-669030
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If tan(A + B) = √3 and tan (A - B)= \(\frac{1}{\sqrt{3}}\); 0º < (A + B) < 90º; A > B, then the values of A and B are respectively.

pipeline-443652
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If 13 sinθ = 2, then the value of \(\frac{3tanθ + √13sinθ}{√13cosθ - 3tanθ}\) is:

pipeline-664918
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Find the exact value of cos 120°.

pipeline-462692
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If sec2 α + cosα = 5/2 and 0° ≤ α ≤ 90°, then find the value of α.

pipeline-304541
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If tan θ + cot θ = 6, then the value of tan2θ + cot2θ is ____ .

pipeline-668733
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If a cot ø + b cosec ø = p and b cote ø + a cosec ø = q then p2 - q2 is equal to______.

pipeline-462573
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Evaluate the following.

sin 25° sin 65° – cos 25° cos 65°.

pipeline-443635
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(sin ø + cosec ø )2 + (cos ø + sec ø )2 = ?

pipeline-462576
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If (sin x + sin y) = a and (cos x + cos y) = b, then find the value of (sin x sin y + cos x cos y).

pipeline-666128
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Find the value of cosecθ (1 − cosθ) (cosecθ + cotθ).

pipeline-665984
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If sin α = \(\frac{5}{13}\) then the value of cosα . cosecα . cotα is

pipeline-666025
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Cosec (90 - θ) = ?

pipeline-33740
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If sin A+ sin2 A = 1 , then the value of cos4 A + cos6 A is:

pipeline-573439
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If Sin x = 4/5, then Sec2x - 1 = ?

pipeline-33102
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If sin θ \(=\frac{1}{2}\), then the value of (3cos θ - 4 cos3 θ) is:

pipeline-392303
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Simplify the following.

cot13°.cot27°.cot45°.cot63°.cot77° = ?

pipeline-392290
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If cot A = 15/8, then what will be the value of tan 2A?

pipeline-392893
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What is the value of \({{cos37°} \over sin53°}?\)

pipeline-393105
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Find the value of \(\frac{\cos37^0}{\sin53^0}\) - cos47° cosec 43°

pipeline-574027
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If tan A = \(\frac{4}{3},0 ≤ A ≤ 90°,\)then find the value of sin A.

pipeline-568011
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If cot B = 9, then what will be the value of sec2 B?

pipeline-392669
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What is the value of cos215°?

pipeline-392077
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If cosA = \(\frac{1}{11}\), then find the value of cot A.

pipeline-574716
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The value of \(\sqrt{{1+cosA} \over 1-cosA}\)   is:

pipeline-389091
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Δ ABC is a right - angle triangle at B. If tan A = 5/12, then sin A + sin B + sin C will be equal to:

pipeline-389118
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If sin q + cos q  = \(\frac{(√3-1)}{(2√2)}\) then what is the value of tan q + cotq ?

pipeline-389990
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If θ is an acute angle and tanθ + cotθ = 2, then the value of tan2θ + cot2θ + 2 tan5θcot4θ is:

pipeline-390736
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In a right-angled triangle PQR, right-angled at Q, the length of the side PR is 17 units, length of the base QR is 8 units, and length of the side PQ is 15 units. If ∠RPQ = α, then sinα + cosα is:

pipeline-387361
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If tan A = \(\frac{2}{3}\), then what is the value of the following?

\((5 sin^2 A - 2 cos^2A) \div(15sin^2A + 3cos^2A)\)

pipeline-390731
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Find the value of sin(90o - 2θ) + 1

pipeline-22292
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Find the value of \({{cos 65°} \over sin25°}\) + \({{5sin19°} \over cos 71°}\) - \({{3cos 28°} \over sin62°}\)

pipeline-569502
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\(\cos^235^ \circ + \cos55^ \circ.\sin 35^\circ + \frac {\tan 34^\circ}{\cot 56^\circ}\) = _________________

pipeline-390739
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The value of (1+ sin4A - cos4A) cosec2A is:

pipeline-569377
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What will be the value of sin 10° – 4/3 sin3 10°?

pipeline-392339
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In the right-angled triangle, ABC, \(\angle \)B = 90° and angle A and angle C are acute angles. If cosecA = \(2\sqrt{2}\), then find the value of sinA . cosC + cosA . sinC.

pipeline-668449
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If cot θ = \({{4} \over 3}\), 0 < θ < 90°, 5pcos2θ sinθ = cot2θ, then the value of p is:

pipeline-569523
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If θ is an acute angle and sin θ + cosec θ = 2, then the value of sin5θ + cosec5θ is:

pipeline-568008
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If cos A = \({15{} \over 17}\), 0 < A < 90°, then the value of Cot(90° - A) is:

pipeline-569487
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Find the value of tan 3θ if sec 3θ = cosec (4θ - 15˚).

pipeline-392063
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What will be the value of cos x cosec x – sin x sec x?

pipeline-390872
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sin290o + cosec290o - cot245o = ?

pipeline-33693
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Solve the following to find its value in terms of trigonometric ratios.

(sin A + cos A)(1 – sin A cos A)

pipeline-392294
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Find the value of (tan2 θ + tan4 θ).

pipeline-568076
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