Q7 of 90 Page 9

Prove that:

Take L.H.S.




= tan x tan (60° - x) tan (60° + x)



Multiplying & Dividing by 2:



{∵ 2 sin A sin B = cos (A – B) – cos (A + B) &


2 cos A cos B = cos (A + B) + cos (A – B)}




{cos (-A) = cos A}



{cos (180° - A) = - cos A}




Multiplying & Dividing by 2:



{∵ 2 cos A sin B = sin (A + B) – sin (A – B) &


2 cos A cos B = cos (A + B) + cos (A – B)}







= tan 3x


= R.H.S.


Hence Proved


More from this chapter

All 90 →
5

Prove that:

 6

Show that

i. sin A sin (B – C) + sin B sin (C – A) + sin C sin (A – B) = 0


ii. sin (B – C) cos (A – D) + sin (C – A) cos(B – D) + sin(A – B) cos(C – D) = 0

 8

1

Express each of the following as the product of sines and cosines:

i. sin 12x + sin 4x


ii. sin 5x – sin x


iii. cos 12x + cos 8x


iv. sin 2x + cos 4x