Prove that cos theta -2cos^3 theta / 2 sin ^3 theta - sin theta = cot theta
class 10
Answers
Answered by
1
Answer:
Step-by-step explanation:
L.H.S. = ( cos θ - 2cos³ θ ) / ( 2sin³ θ - sin θ )
= cos θ ( 1 - 2 cos² θ ) / sin θ ( 2sin² θ - 1 )
= ( cos θ ) [ - ( 2 cos² θ - 1 ) ] / ( sin θ ) [ - ( 1 - 2 sin² θ ) ]
= ( cos θ / sin θ ) ( - cos 2θ / - cos 2θ ) [∵cos 2θ = 2 cos² θ - 1 and 1- 2 sin² θ]
= cot θ
= R.H.S.
∴L.H.S. = R.H.S.
Hence, it is proved.
Similar questions