EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Inverse Trigonometric Functions>JEE Advanced Paper 2 - 2015>Q 2

HARD

JEE Advanced

IMPORTANT

Earn 100

If $α = 3 \sin^{- 1} (\frac{6}{11}) & β = 3 \cos^{- 1} (\frac{4}{9}),$ where the inverse trigonometric functions take only the principal values, then the correct options(s) is(are)

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Important Questions on Inverse Trigonometric Functions

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Inverse Trigonometric Functions>JEE Advanced Paper 2 - 2018>Q 1

For any positive integer

n

, define

f_{n} : (0, \infty) \to R

as

f_{n} (x) = \sum_{i = 1}^{n} \tan^{- 1} (\frac{1}{1 + (x + j) (x + j - 1)})

for all

x \in (0, \infty)

.

$($ Here, the inverse trigonometric function $\tan^{- 1} x$ assumes values in $(- \frac{π}{2}, \frac{π}{2})$ $)$

Then, which of the following statement(s) is (are) TRUE?

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Inverse Trigonometric Functions>JEE Advanced Paper 2 - 2015>Q 2

If

α = 3 \sin^{- 1} (\frac{6}{11}) & β = 3 \cos^{- 1} (\frac{4}{9}),

where the inverse trigonometric functions take only the principal values, then the correct options(s) is(are)