Commerce (English Medium) Class 11 - CBSE Question Bank Solutions

If α and β are acute angles satisfying \[\cos 2 \alpha = \frac{3 \cos 2 \beta - 1}{3 - \cos 2 \beta}\] , then tan α =

If  \[\tan \frac{x}{2} = \frac{\sqrt{1 - e}}{1 + e} \tan \frac{\alpha}{2}\] , then \[\cos \alpha =\]

If  \[\left( 2^n + 1 \right) x = \pi,\] then \[2^n \cos x \cos 2x \cos 2^2 x . . . \cos 2^{n - 1} x = 1\]

If \[\tan x = t\] then \[\tan 2x + \sec 2x =\]

The value of \[\cos^4 x + \sin^4 x - 6 \cos^2 x \sin^2 x\] is 

The value of \[\cos \left( 36°  - A \right) \cos \left( 36° + A \right) + \cos \left( 54°  - A \right) \cos \left( 54°  + A \right)\] is 

The value of \[\tan x \tan \left( \frac{\pi}{3} - x \right) \tan \left( \frac{\pi}{3} + x \right)\] is

The value of \[\tan x + \tan \left( \frac{\pi}{3} + x \right) + \tan \left( \frac{2\pi}{3} + x \right)\] is 

The value of \[\frac{\sin 5 \alpha - \sin 3\alpha}{\cos 5 \alpha + 2 \cos 4\alpha + \cos 3\alpha} =\]

If \[n = 1, 2, 3, . . . , \text{ then }  \cos \alpha \cos 2 \alpha \cos 4 \alpha . . . \cos 2^{n - 1} \alpha\] is equal to

If \[\text{ tan } x = \frac{a}{b}\], then \[b \cos 2x + a \sin 2x\]

If \[\tan\alpha = \frac{1}{7}, \tan\beta = \frac{1}{3}\], then

\[\cos2\alpha\]   is equal to

The value of `cos^2 48^@ - sin^2 12^@` is ______.

If A = cos²θ + sin⁴θ for all values of θ, then prove that `3/4` ≤ A ≤ 1.

The greatest value of sin x cos x is ______.

The value of sin 20° sin 40° sin 60° sin 80° is ______.

The value of `cos  pi/5 cos  (2pi)/5 cos  (4pi)/5 cos  (8pi)/5`  is ______.

Prove that sin 4A = 4sinA cos³A – 4 cosA sin³A

If tanθ + sinθ = m and tanθ – sinθ = n, then prove that m² – n² = 4sinθ tanθ 
[Hint: m + n = 2tanθ, m – n = 2sinθ, then use m² – n² = (m + n)(m – n)]