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. (1 + tan^2 A /1+cot^2 A) = (1 - tan A/1- cot A)^2=tan^2 A

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

          (x) (\frac{1+\tan ^{2}A}{1+\cot ^{2}A})= (\frac{1-\tan A}{1-\cot A})^{2}= \tan ^{2}A
 

Answers (1)

best_answer

We need to prove,
(\frac{1+\tan ^{2}A}{1+\cot ^{2}A})= (\frac{1-\tan A}{1-\cot A})^{2}= \tan ^{2}A

Taking LHS;

\\\Rightarrow \frac{1+\tan ^{2}A}{1+\cot ^{2}A} = \frac{\sec^2A}{\csc^2A}=\tan^2A

Taking RHS;

\\=(\frac{1-\tan A}{1-\cot A})^2\\\\= (\frac{1-\sin A/\cos A }{1-\cos A /\sin A})^2\\\\ = \frac{(\cos A -\sin A)^2(\sin^2A)}{(\sin A-\cos A)^2(\cos^2A)}\\\\ =\tan^2A

LHS = RHS

Hence proved.

Posted by

manish

View full answer

Similar Questions

Trending Articles/News

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 LIVE: 10th phase 2 marksheet for over 6 lakh on DigiLocker soon
anam-khan

CBSE 10th Second Board Result 2026 Highlights: Phase 2 Class 10 scores soon

Latest Question