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

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

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:

Find the value of the following expression.

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

The value of \((\frac{1}{sin\theta} + \frac{1}{tan\theta}) (\frac{1}{sin\theta} - \frac{1}{tan\theta})\) is:

Given that A and B are second quadrant angles, sin A =\(\frac{1}{3}\)  and sin B = \(\frac{1}{5}\) , then find the value of cos(A - B)

Evaluate \(7\left ( \frac{cosec 24^\circ}{sec 66^\circ} \right )^3+ 8\left (\frac{cot 37^\circ}{tan 53^\circ} \right )^4-\left ( 2\frac{sec 14^\circ}{cosec 76^\circ} \right )^2+ \left ( -3\frac{tan82^\circ}{cot8^\circ} \right )^3\)

Find the value of 2cosec² 23° cot²67° - sin²23° - sin²67° - cot²67°.

If \(\frac{cos(x+A)}{a} = \frac{cos(x+2A)}{b} = \frac{cos(x+3A)}{c}\) and A = 60° , X = 15°, then the value of \((\frac{a+c}{b})^2 + (\frac{a-c}{b})^2\) is ______________________ :

\([\frac{cosec31^{\circ}-sec59^{\circ}}{(sin18^{\circ}÷cos72^{\circ})}×\frac{tan26^{\circ}}{cot64^{\circ}}]+[\frac{tan30^{\circ}+tan15^{\circ}}{(1-tan30^{\circ}tan15{\circ})}]=\) _______________.

The value of \((tan25^ocot65^o-cosec^265^o)+cot^261^o-sec^229^o\over sin^25^o+sin^27^o+sin^29^o+...+sin^285^o\)is:

If tanθ = \(2 \over \sqrt{11}\), 0° < θ < 90° , then the value of \(\frac{2cosec²θ - 3sec²θ}{3cosec²θ + 4sec²θ}\) is equal to:

The value of the expression  \( \frac{4sin^230^\circ+cos^260^\circ- tan^245^\circ}{2sin60^\circ cos30^\circ-tan45^\circ}\)is :

If \( {sec \theta + tan \theta \over sec \theta - tan \theta} = {5 \over 3}\) 0°< θ < 90°, then what is the value of (cosec θ + cos θ + cot θ)?

The value of \(sin^2 \frac{2\pi}{3} + cos^2\frac{5\pi}{6} - tan^2 \frac{3\pi}{4} is :\)

If cosθ = sin(2θ) ≠ 0 , what is the value of cos⁴θ + sin⁴ θ + cos³θ + sin³θ + sin²θ + cos²θ + sinθ + cosθ?

If 14 sin²θ + 3 sinθ - 5 = 0, 0° < θ < 90°, then the value of \(sec2θ+cot2θ\over{cosec2θ+tan2θ}\) is:

If (cosecθ - sinθ) (secθ - cosθ) (tanθ + cotθ) - tanθ= 0, 0°< θ < 90°, then the value of \(\frac{2cos\theta + sin\theta}{5cos\theta-sin\theta}\) is:

If cos²θ – sin²θ – 3cosθ + 2 = 0, 0° < θ < 90° ,then what is the value of 5cosθ - \( {tan\theta{} \over 2}\)

\(({ {\sqrt {3} + 2sin P} \over {1 - 2cos P} }) ^ {3}\) + \(({ {1 + 2cos P} \over {\sqrt {3} - 2sin P} }) ^ {3}\) = ?

What is the value of \(\frac{tan9^\circ tan23^\circ tan60^\circ tan67^\circ tan81^\circ}{cosec^272^\circ+cos^215^\circ-tan^218^\circ+cos^275^\circ}\)

If \(\frac{cos\theta}{1-sin\theta} + \frac{cos\theta}{1+sin\theta}\) = 4, 0⁰ < θ < 90⁰ , then what is the value of (secθ + cosecθ + cotθ) ?

The value of \(tan^2(22^o-θ)-tan(θ+68^o)-cosec^2(68^o+θ)+cot(22^o-θ)\over3(cot^252^o-sec^238^o)+2(cosec^228^o-tan^262^o)\) is:

If sin\(\theta\) + tan\(\theta\) = p and tan\(\theta\) - sin\(\theta\) = q, then which of the relations satisfies for given values of p and q?

If A, B, and C are the acute angles, such that tan(A + B - C) = \(\frac{1}{\sqrt3}\), cos(B + C - A) = \(\frac{1}{2}\), and sin(C + A - B) = \(\frac{1}{\sqrt2}\). The value of A + B + C will be equal to:

If m=sec \(\theta\)-tan \(\theta\) and n = cosec \(\theta\)+ cot \(\theta\), then what is the value of m + n(m-1)?

If cosecθ = 3x and cotθ =\(\frac{3}{x}\) , (x ≠ 0) then the value of 6\(({x^2 + {1} \over {x^2}})\) is:

(4 cos²9° - 3) (4 cos²27° - 3) = ?

If \(a\cos\theta - b\sin\theta = \sqrt{a^2+b^2}\) & \(\frac{\cos^2\theta}{p^2} + \frac{\sin^2\theta}{q^2} = \frac{1}{a^2+b^2}\) then the correct relationship is

Find the value of \(\frac{\cot\theta+cosec\theta-1}{\cot\theta-cosec\theta+1}\)

If \(\sin\theta + \cos\theta = K\) & \(\sec\theta + cosec\,\theta = m\), then find \(m(K^2 - 1)\)?

Simplify: (\(1\over tanθ\) + \(1\over cotθ\))(cosecθ - cotθ)(\(1+cosθ\over cosθ\))

The value of 3 + tan²∅ + cot²∅ − sec²∅ cosec²∅ is:

Simplify the following: (1 + cot²θ)(1 − cos θ)(1 + cos θ)

The value of \((\sin 37^\circ \cos 53^\circ + \cos 37^\circ \sin 53^\circ) - \frac{4 \cos^2 37^\circ - 7 + 4 \cos^2 53^\circ}{\tan^2 47^\circ + 4 - \operatorname{cosec}^2 43^\circ}\) is:

Consider the following:
(I) cos⁴θ - sin⁴θ = \(2tanθ\over{1-tan^2θ}\), 0 < θ < π/2
(II) cosecθ + cotθ = \(1\over cosecθ-cotθ\),0 < θ < π/2
(III) cos²θ - sin²θ = \(1-tan^2θ\over1+tan^2θ\), 0 < θ < π/2
Which option is correct?

If the roots of the quadratic equation x² + px + q = 0 are tan21° and tan 24°, respectively, then find the value of 3 + q – p?

Find the value of \((\sec A - cosec A)-\frac{1}{\sec A+\tan A}+\frac{1}{cosec A-cot A}\).

If cosecx + cosec²x = 1, then cot⁶x - 3cot⁸x + 3cot¹⁰x - cot¹²x = ?

If sin \({23\pi\over24}={{\sqrt{{2\sqrt p-\sqrt q-1}\over 4\sqrt r}}}\), then find p² + q² - r².

The value of sin18° is given as \( \frac{\sqrt{5}-1}{4}\). Using the value, find sin54°?

If (a + b) sinθ + (a - b) cosθ = 3, (a + b) cosθ + (a - b) sinθ = 4 then find (a² + b²)?

What is the value of \( \left (\frac{1+sec^2A}{1+cos^2A} \right ) \left (\frac{1+sin^2A}{1+cosec^2A} \right )\)?

Find (1 + tan20°)(1 + tan24°)(1 + tan25°)(1 + tan21°)?

If sin x = 1/2, then find the value of (sec⁴x + cosec⁴x) − (tan⁴x + cot⁴x).

If sec⁴θ - tan⁴θ = 11, then find the value of sinθ + cosecθ?

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

If cos²θ - sin²θ = tan²α, then cosθ cosα = ?

If (1 + tanθ)(1 + tan5θ) - 2 = 0, θ ϵ (0,π/16) , then find sin12θ + cos12θ ?

cot³θ/cosec²θ + tan³θ/sec²θ + 2sinθcosθ is equal to?