Tamil Nadu Board of Secondary EducationHSC Arts Class 12th

Find the value of tan-1(3)-sec-1(-2) - Mathematics

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Sum

Find the value of `tan^-1 (sqrt(3)) - sec^-1 (- 2)`

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Solution

x = `tan^-1 (sqrt(3))`

tan x = `sqrt(3) = tan  pi/3`

x = `pi/3`

y = `sec^-1(- 2)`

sec y = ` - 2 = - sec  pi/3`

sec y = `sec(pi - pi/3)`

sec y = `sec(2 pi/3)`

y = `(2  pi/3)`

`tan^-1 (sqrt(3)) - sec^-1(- 2) = pi/3 - (2pi)/3`

= `(pi - 2pi)/3`

= `- pi/3`

Concept: Principal Value of Inverse Trigonometric Functions
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APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 12th Mathematics Volume 1 and 2 Answers Guide
Chapter 4 Inverse Trigonometric Functions
Exercise 4.4 | Q 2. (i) | Page 155
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