The value of tan−1(21tan2A)+tan−1(cotA)+tan−1(cot3A) for 0<A<4π is?

We have,tan−1 (21tan 2A)+tan−1 (cot A)+tan−1 (cot 3A) tan−1 (21tan 2A)+π+tan−1 (1−cot 4Acot A+cot 3A ) tan (1−tan Atan A )+π+tan−1 (1−cot 2Acot A ) =π+tan−1 (tan 2A−12tan A )+tan−1 (1−tan 2Atan A ) =π =4tan−1 (1) Hence,optionAisthecorrectanswer.

Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Home

The value of ^{-1}({1}{2} 2A)+^{-1}( A)+^{-1}(^3 A) for 0 < A

Question

The value of $tan^{- 1} (\frac{1}{2} tan 2 A) + tan^{- 1} (cot A) + tan^{- 1} (cot^{3} A)$ for $0 < A < \frac{π}{4}$ is?

4 tan^{- 1} 1

2 tan^{- 1} 2

0

N o n e

Views: 882 students

Found 2 tutors discussing this question

Elijah Discussed

The value of

tan^{- 1} (\frac{1}{2} tan 2 A) + tan^{- 1} (cot A) + tan^{- 1} (cot^{3} A)

for

0 < A < \frac{π}{4}

is?

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

We have,

tan^{- 1} (\frac{1}{2} tan 2 A) + tan^{- 1} (cot A) + tan^{- 1} (cot 3 A) tan^{- 1} (\frac{1}{2} tan 2 A) + π + tan^{- 1} (\frac{c o t A + c o t ^{3} A}{1 - c o t ^{4} A}) tan (\frac{t a n A}{1 - t a n A}) + π + tan^{- 1} (\frac{c o t A}{1 - c o t ^{2} A}) = π + tan^{- 1} (\frac{t a n A}{t a n ^{2} A - 1 ^{2}}) + tan^{- 1} (\frac{t a n A}{1 - t a n ^{2} A}) = π = 4 tan^{- 1} (1) He n ce, o pt i o n A i s t h e correc t an s w er .

Was this solution helpful?

150

Report

One destination for complete JEE/NEET preparation

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our maths tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	The value of $tan^{- 1} (\frac{1}{2} tan 2 A) + tan^{- 1} (cot A) + tan^{- 1} (cot^{3} A)$ for $0 < A < \frac{π}{4}$ is?
Answer Type	Text solution:1
Upvotes	150

The value of tan−1(21​tan2A)+tan−1(cotA)+tan−1(cot3A) for 0<A<4π​ is?

Text solutionVerified

Practice questions from similar books

The value of $tan^{- 1} (\frac{1}{2} tan 2 A) + tan^{- 1} (cot A) + tan^{- 1} (cot^{3} A)$ for $0 < A < \frac{π}{4}$ is?