Home
Class 12
MATHS
Prove that: cos e c(tan^(-1)("cos"(cot^(...

Prove that: `cos e c(tan^(-1)("cos"(cot^(-1)("sec"(sin^(-1)a)))))=sqrt(3-a^2),` where `a in [0,1]`

Text Solution

Verified by Experts

Here `x = cosec (tan^(-1) (cos (cot^(-1) (sec (sin^(-1) a)))))`
`=cosec (tan^(-1) (cos (cot^(-1) ((1)/(sqrt(1 - a^(2)))))))`
`= cosec(tan^(-1) ((1)/(sqrt(2 - a^(2)))))`
`= sqrt(3 - a^(2))`
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 7.4|12 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 7.5|13 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 7.2|6 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise JEE Previous Year|20 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

Similar Questions

Explore conceptually related problems

Prove that: csc(tan^(-1)(cos(cot^(-1)(sec(sin^(-1)a)))))=sqrt(3-a^(2)) where a in[0,1]

Prove that cos tan^(-1)sin cot^(-1)x=sqrt((x^(2)+1)/(x^(2)+2))

Prove that sec^(2)(tan^(-1)2)+cos ec^(2)(cot^(-1)3)=15

Prove that : sin cot^(-1) tan cos^(-1) x=x

If cos(tan^(-1)(sin(cot^(-1)sqrt(3))))=y, then

Prove that cos (tan^(-1) (sin (cot^(-1) x))) = sqrt((x^(2) + 1)/(x^(2) + 2))

Prove that sin cot^(-1) tan cos^(-1) x = sin cosec^(-1) cot tan^(-1) x = x, " where " x in [0,1]

If =cos ec[tan^(-1){cos(cot^(-1)(sec(sin^(-1)a)))}] and y=sec[cot^(-1){sin(tan^(-1)(cos ec(cos^(-1)a)))}]

The number of solutions of cos(2sin^(-1)(cot(tan^(-1)(sec(6csc^(-1)x))))+1=0 where x>0 is