Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Prove the following identities, where the angles involved are acute angles for which the expressions are defined. sin Theta- 2 sin^3 Theta/ 2 cos^3 Theta - cos Theta = tan Theta

5. Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

   (vii)\frac{\sin \theta -2\sin ^{3}\theta }{2\cos ^{3}\theta -\cos \theta }= \tan \theta

Answers (1)

best_answer

We need to prove -
\frac{\sin \theta -2\sin ^{3}\theta }{2\cos ^{3}\theta -\cos \theta }= \tan \theta

Taking LHS;
[we know the identity \cos2\theta = 2\cos^2\theta-1=\cos^2\theta-\sin^2\theta]

\\\Rightarrow \frac{\sin \theta(1 -2\sin ^{2}\theta) }{\cos\theta(2\cos ^{2}\theta -1) }\\\\ \Rightarrow \frac{\sin\theta(\sin^2\theta+\cos^2\theta-2\sin^\theta)}{\cos\theta.\cos2\theta}\\\\ \Rightarrow \frac{\sin\theta.\cos2\theta}{\cos\theta.\cos2\theta}\\\\ \Rightarrow \tan\theta =RHS

Hence proved.

Posted by

manish

View full answer

Similar Questions

Trending Articles/News

anam-khan

Supreme court asks centre not to introduce third language in class 9 under CBSE curriculum
anam-khan

CBSE issues study guidelines for three-language scheme; mandates passing R3 for Classes 9, 10 students
anam-khan

CBSE Class 10 Second Board Result 2026 (Out) LIVE: 10th session 2 marksheet out at Digilocker; official link

Latest Question