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

If a = b \[\cos \frac{2\pi}{3} = c \cos\frac{4\pi}{3}\] then write the value of ab + bc + ca.  

If A + B = C, then write the value of tan A tan B tan C.

If sin α − sin β = a and cos α + cos β = b, then write the value of cos (α + β). 

If tan \[\alpha = \frac{1}{1 + 2^{- x}}\] and \[\tan \beta = \frac{1}{1 + 2^{x + 1}}\] then write the value of α + β lying in the interval \[\left( 0, \frac{\pi}{2} \right)\] 

The value of \[\sin^2 \frac{5\pi}{12} - \sin^2 \frac{\pi}{12}\] 

If A + B + C = π, then sec A (cos B cos C − sin B sin C) is equal to

tan 20° + tan 40° + \[\sqrt{3}\] tan 20° tan 40° is equal to 

If \[\tan A = \frac{a}{a + 1}\text{ and } \tan B = \frac{1}{2a + 1}\] 

If 3 sin x + 4 cos x = 5, then 4 sin x − 3 cos x =

If in ∆ABC, tan A + tan B + tan C = 6, then cot A cot B cot C =

tan 3A − tan 2A − tan A =

If A + B + C = π, then \[\frac{\tan A + \tan B + \tan C}{\tan A \tan B \tan C}\] is equal to

If \[\cos P = \frac{1}{7}\text{ and }\cos Q = \frac{13}{14}\], where P and Q both are acute angles. Then, the value of P − Q is

If cot (α + β) = 0, sin (α + 2β) is equal to

The value of \[\cos^2 \left( \frac{\pi}{6} + x \right) - \sin^2 \left( \frac{\pi}{6} - x \right)\] is

If tan θ₁ tan θ₂ = k, then \[\frac{\cos \left( \theta_1 - \theta_2 \right)}{\cos \left( \theta_1 + \theta_2 \right)} =\]

If sin (π cos x) = cos (π sin x), then sin 2x = ______.

If \[\tan\theta = \frac{1}{2}\] and \[\tan\phi = \frac{1}{3}\], then the value of \[\tan\phi = \frac{1}{3}\] is 

The value of cos (36° − A) cos (36° + A) + cos (54° + A) cos (54° − A) is