RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 4. Inverse Trigonometric Functions

Subject: Maths - Class 12th

Q. No. 30 of MCQ

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30

Choose the correct answer

If tan–1 (cot θ) = 2 θ, then θ =


We are given that,

tan-1 (cot θ) = 2θ


We need to find the value of θ.


We have,


tan-1 (cot θ) = 2θ


Taking tangent on both sides,


⇒ tan [tan-1 (cot θ)] = tan 2θ


Using property of inverse trigonometry,


tan(tan-1 A) = A


⇒ cot θ = tan 2θ


Or,


⇒ tan 2θ = cot θ


Using the trigonometric identity,




Using the trigonometric identity,




By cross-multiplying,


⇒ tan θ × 2 tan θ = 1 – tan2 θ


⇒ 2 tan2 θ = 1 – tan2 θ


⇒ 2 tan2 θ + tan2 θ = 1


⇒ 3 tan2 θ = 1




And .



Thus,


Chapter Exercises

Exercise 4.1
Exercise 4.2
Exercise 4.3
Exercise 4.4
Exercise 4.5
Exercise 4.6
Exercise 4.7
Exercise 4.8
Exercise 4.9
Exercise 4.10
Exercise 4.11
Exercise 4.12
Exercise 4.13
Exercise 4.14
Very short answer
MCQ

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