Home
Class 12
MATHS
Find the value of sec^(-1)(-2)+tan^(-1)(...

Find the value of `sec^(-1)(-2)+tan^(-1)(-1/sqrt3)`

Text Solution

Verified by Experts

`sec^(-1)(-x)=pi-sec^(-1)x`
`sec^(-1)(-2)=pi-sec^(-1)2`
and the principal value of `sec^(-1)2" is " pi/3`
`:. Sec^(-1)(-2)=pi/-pi/3`
`=(2pi)/3`
Also, `tan^(-1)(-1/sqrt3)=-tan^(-1)(1/sqrt3),( :' tan^(-1)(-x)=-tan^(-1)x)`
`=-pi/6`
`:. sec^(-1)(-2)+tan^(-1)(-1/sqrt3)`
`=(2pi)/3-pi/6=pi/2`
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    AAKASH INSTITUTE|Exercise TRY YOURSELF|21 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    AAKASH INSTITUTE|Exercise ASSIGNMENT (SECTION - A)(OBJECTIVE TYPE QUESTIONS (ONE OPTION IS CORRECT))|45 Videos

  • INTEGRALS

    AAKASH INSTITUTE|Exercise Try yourself|50 Videos

  • LIMITS AND DERIVATIVES

    AAKASH INSTITUTE|Exercise Section - j|3 Videos

Similar Questions

Explore conceptually related problems

Find the value of tan.[cos^(-1)(1/2)+tan^(-1)(-1/(sqrt(3)))]

Find the value of tan^(-1)sqrt(3)-cot^(-1)-sqrt(3)

Find the value of tan[cos^(-1) (1/2) + tan^(-1) ( - 1/sqrt3)]

Find the value of sec(tan^(-1)((y)/(2)))

Find the principal value of sin^(-1)(-1/sqrt2)+tan^(-1)(-1/sqrt3)+sec^(-1)(2)

Find the principal value of sec^(-1)((2)/(sqrt(3)))+tan^(-1)(-sqrt(3))

Find the value of (2tan^(-1)((1)/(sqrt(3)))+cos(tan^(-1)(2sqrt(2)))

Find the value of : tan^(-1) ((-1)/(sqrt(3)))+cos^(-1)((-sqrt(3))/2)+sin^(-1)(1/2)

Find the principal value of tan^(-1)(-1/sqrt3) .

Find the value of : tan^(-1)(- 1/sqrt(3))