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Question

cot-1(3)+cosec-1(√5)=


A

Ο€3

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B

Ο€4

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C

Ο€6

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D

Ο€2

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Solution

The correct option is B

Ο€4


Explanation for the correct option:

Step 1. Suppose cosecβˆ’15=ΞΈ

β‡’ cosecΞΈ=5

Given, cot-1(3)+cosec-1(√5) …..(1)

∡cot2ΞΈ=cosec2ΞΈβˆ’1

=5βˆ’1

=4

∴ cotθ=2

β‡’ΞΈ=cotβˆ’12

∴cosecβˆ’15=ΞΈ

β‡’ cosec-15=cotβˆ’12

Step 2. Put the value of cosec-15 in Equation (1):

β‡’cotβˆ’13+cotβˆ’12

β‡’tanβˆ’113​+tanβˆ’112

β‡’tanβˆ’1​13​+121βˆ’13​.12 ∡tan-1A+tan-1B=tan-1(A+B1-A.B)

β‡’tanβˆ’15656

β‡’tanβˆ’1(1)

β‡’Ο€4

Hence, Option β€˜B’ is Correct.


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