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

Show that:
sin A sin (B − C) + sin B sin (C − A) + sin C sin (A − B) = 0

Show that:
sin (B − C) cos (A − D) + sin (C − A) cos (B − D) + sin (A − B) cos (C − D) = 0

Prove that:
\[\tan x \tan \left( \frac{\pi}{3} - x \right) \tan \left( \frac{\pi}{3} + x \right) = \tan 3x\]

If α + β = \[\frac{\pi}{2}\], show that the maximum value of cos α cos β is \[\frac{1}{2}\].

Express each of the following as the product of sines and cosines:
sin 12x + sin 4x

Express each of the following as the product of sines and cosines:
sin 5x − sin x

Express each of the following as the product of sines and cosines:
 cos 12x + cos 8x

Express each of the following as the product of sines and cosines:
 cos 12x - cos 4x

Express each of the following as the product of sines and cosines:
sin 2x + cos 4x

Prove that:
sin 38° + sin 22° = sin 82°

Prove that:
 cos 100° + cos 20° = cos 40°

Prove that:
sin 50° + sin 10° = cos 20°

Prove that:
 sin 23° + sin 37° = cos 7°

Prove that:
sin 105° + cos 105° = cos 45°

Prove that:
sin 40° + sin 20° = cos 10°

Prove that:
 cos 55° + cos 65° + cos 175° = 0

Prove that:
 sin 50° − sin 70° + sin 10° = 0

Prove that:
 cos 80° + cos 40° − cos 20° = 0

Prove that:
cos 20° + cos 100° + cos 140° = 0

Prove that:
\[\sin\frac{5\pi}{18} - \cos\frac{4\pi}{9} = \sqrt{3} \sin\frac{\pi}{9}\]