If \({2+3 i\sin\theta}\over{1-2i\sin\theta}\) the expression is purely imaginary; then find the value of θ.

\({{cos20°} \over sin70°}+{{cos\theta} \over sin(90°-\theta)}=\)________________.

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

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

If cos(3α) = sin(α — 22°), where 3α < 90°, then what is the value of α ?

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

cosec 2910°+ sec 4260° + tan 2565° + cot 1755° = ?

If sinA + cosecA = 2, then what is the value of sin²⁹A + cosec²⁹A?

If cos²A + cos²B = 0, then what is the value of cot³A + sin²B?

If (sin 120° - cos 300°)/(tan 240° + cos 360°) = a², then what is the value of 2a + 1? (a > 0)

Which of the following is equivalent to the trigonometric expression given below?

{sin x × (1 + cos x)}/(1 + cos x - cos² x - cos³ x)

If x = p secA cosB, y = q secA sinB & z = r tanA, then what is the value of \(\frac{x^2}{p^2} + \frac{y^2}{q^2} - \frac{z^2}{r^2}\)?

Find the value of 2sin15°cos75° + (tan 22° – cot 68°) × sin 11°.

For two acute angles x and y, what is the maximum value of the following trigonometric expression?

(sin² x – 5 sin x + 3) + (cos⁴ y + sin⁴y – 2 sin²y cos²y)

Find the value of (sin⁴ x + cos² x)/(cos⁴ x + sin² x).

What is the maximum value of the following trigonometric expression?

35 cosα cosβ + 84 cos α sinβ + 120 sinα cosβ + 288 sinα sinβ,

where α and β are any angles between 0° and 360°.

Simplify - \({15\times (\sec^2(90^{\circ}-45^{\circ}) - \cot^245^{\circ})\over2(\sin^248^{\circ} + \sin^242^{\circ})} - {2 (\cos^233^{\circ} + \cos^257^{\circ})\over \cos60^{\circ}}\)

If cos θ = 12/13 and cos Ø = 4/5 then, find the value of cot(θ + Ø).

In △PQR, tanP = 5 cm, tanR = 4 cm . What will be the value of sinQ × cosQ?

If 1 + sin²θ - 3 sinθ cosθ = 0, then find the value of cotθ (θ ≠ 45°)?

{(3sin x – 4sin 3x)/(3sin y – 4sin 3y)}² + 1

If x and y are complementary angles, what is the value of the following expression?

What will be the value of cosec(- 45°) + sec (π/2 - 45°) - sin(- 90°) - tan²(- 30°)?

If (a² - b²) sinθ + 2ab cosθ = a² + b², then find the value of secθ + tanθ?

If r = 15(sinθ + cosθ) and s = 16(sinθ - cosθ), then the value of \(\frac{r^2}{15^2} + \frac{s^2}{16^2}\)  is ______ .

In ΔABC, ∠B = 90°, AC = 29 cm, and BC = 20 cm. Then \((1 - sin A + cos A)\over(1 + sin A + cos A)\) is equal to:

If 6 + 8tanθ = secθ and 8 – 6tanθ = k secθ, then what is the value of k²?

The expression (cos⁶ θ + sin⁶ θ - 1) (tan ²θ + cot² θ + 2) + 1 is equal to:

The value of cot²46° - sec²44° + (sin 1⁰ + sin²3° + sin²5° + ... + sin²89°) is:

\({{sec} ^ {6} θ - {tan} ^ {6} θ - 3sec ^2 θ tan ^2θ + 1} \over { {cos} ^ {4} θ - {sin} ^ {4} θ + 2sin ^2 2 θ + 2}\) = ?

(1 + sinA)(1 – sinA)(1 + tan²A) is equal to:

Simplify the following expression: \({cosA} \over {1 - tanA}\) + \({sinA} \over {1 - cotA}\) - sinA

For acute angle x, what is the minimum value of the following expression?

sec²x + cot²x (1 + 2tan²x) + 3 

If \(7sin θ + 4cos θ\over 9sin θ - 2cos θ\) = \(5\over4\), then the value of \(tan^2 θ + 5\over tan^2  θ - 5\) is : 

What is the maximum value of 7 cosA + 24 sinA + 32?

The value of [cot²44° - sin²46°]cosec²46°tan²44° is:  

If sin (A + B) = 1 and cos(A - B) = \(\sqrt3 \over 2\) A + B ≤ 90° and A > B, then the \({5sin² B + 4tan² A} \over {2sin B cos A}\) value is: of

If m = a secA and y = b tanA, then find the value of b²m² - a²y²+\(a^2 y^2\over b^2 m^2\)+ cos²A.

If 5 sin²x – 13 sinx + 6 = 0, then what is the value of sec x – tan x?

If \({sin²θ} \over {tan²θ - sin² θ}\) = 5, θ is an acute angle, then the value of \({24sin²θ - 15sec²θ} \over {6cosec² θ - 7cot² θ}\)is:

\(\frac{1+cos4x}{cotx-tanx}\)= ?

If cosA + cos²A = 1 then sin²A + sin⁴A is equal to:

The value of \(\left(\frac{sin\theta}{1+cos\theta}+\frac{1+cos\theta}{sin\theta}\right) \)\(\left(\frac{1}{tan\theta + cot\theta}\right) \)is equal to:

The value of \({tan(45° - α)} \over {cot(45° + α)}\) - \({(cos 19° + sin 71°)(sec 19° + cosec 71°)} \over {tan12° tan 24° tan 66° tan 78°}\) is :

If sin⁶θ + cos⁶θ = sin2θ, then find cos4θ?

If (cos²θ - 1)(2sec²θ) + sec²θ + 2tan²θ = 2, 0° < θ < 90°, then \((secθ + sinθ)\over (cosecθ - cosθ)\)  is equal to:

What is the value of sec²54° - cot²36° + \(\frac{3}{2}\) sin²37° × sec²53° + \(\frac{2}{\sqrt{3}}\)tan60°?

Using trigonometric formulas, find the value of \((\frac{sin(x-y)}{sin(x+y)})\) \((\frac{tan x + tan y}{tan x - tan y})\)

Find the value of the following expression.

12(sin⁴ \(\theta\) + cos⁴ \(\theta \)) + 18(sin⁶ \(\theta \) + cos⁶ \(\theta \)) + 78sin² \(\theta \) cos² \(\theta \)

If  \({{k-kcot^230°} \over 1+cot^230°}\) \(=sin^260°+4tan^245°-cosec^260°\), then the value of k (correct to two decimal places) is:

\(\frac{sin^4 \theta + cos^4 \theta}{1-2sin^2 \theta. cos^2 \theta}=\) ___________.

If \(secθ - 2cosθ = {{7} \over 2}\), where θ is a positive acute angle, then the value of secθ is: