PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions

Prove that:

Prove that:

If tan x = \[x - \frac{1}{4x}\], then sec x − tan x is equal to

If sec \[x = x + \frac{1}{4x}\], then sec x + tan x = 

If \[\frac{\pi}{2} < x < \frac{3\pi}{2},\text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}}\] is equal to

If \[0 < x < \frac{\pi}{2}\], and if \[\frac{y + 1}{1 - y} = \sqrt{\frac{1 + \sin x}{1 - \sin x}}\], then y is equal to

If \[\frac{\pi}{2} < x < \pi, \text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}}\] is equal to

If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then x² + y² + z² is independent of

If tan x + sec x = \[\sqrt{3}\], 0 < x < π, then x is equal to

If tan \[x = - \frac{1}{\sqrt{5}}\] and θ lies in the IV quadrant, then the value of cos x is

If \[\frac{3\pi}{4} < \alpha < \pi, \text{ then }\sqrt{2\cot \alpha + \frac{1}{\sin^2 \alpha}}\] is equal to

sin⁶ A + cos⁶ A + 3 sin² A cos² A =

If \[cosec x - \cot x = \frac{1}{2}, 0 < x < \frac{\pi}{2},\]

If \[cosec x + \cot x = \frac{11}{2}\], then tan x =

If x is an acute angle and \[\tan x = \frac{1}{\sqrt{7}}\], then the value of \[\frac{{cosec}^2 x - \sec^2 x}{{cosec}^2 x + \sec^2 x}\] is

The value of sin²5° + sin²10° + sin²15° + ... + sin²85° + sin²90° is

sin² π/18 + sin² π/9 + sin² 7π/18 + sin² 4π/9 =