Home
Class 12
MATHS
Evaluate: tan{2t a n-1 1/5-pi/4}...

Evaluate: `tan{2t a n-1 1/5-pi/4}`

A

`7/17`

B

`-7/17`

C

`7/12`

D

`-7/12`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `2tan^(-1)1/5=theta`. Then, `tan^(-1)1/5=1/2=theta rArr tan1/2theta=1/5`.
`therefore tantheta=(2tan1/2theta)/(1-tan^(2)1/2theta)=(2 xx 1/5)/(1-1/25)=(2/5 xx 25/24)=5/12`.
`therefore tan[2tan^(-1)1/5-pi/4]=tan(theta-pi/4)=(tantheta-tanpi/4)/(1+tantheta.tanpi/4)`
`=((5/12-1))/((1+5/12 xx 1)0=((-7/12))/((17/12))=-7/17`.
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGNOMETRIC FUNCTIONS

    RS AGGARWAL|Exercise Exercise 4D|6 Videos

  • INTEGRATION USING PARTIAL FRACTIONS

    RS AGGARWAL|Exercise Objective Questions Ii|37 Videos

  • LINEAR DIFFERENTIAL EQUATIONS

    RS AGGARWAL|Exercise Objective Questions|27 Videos

Similar Questions

Explore conceptually related problems

Evaluate: tan{2tan-1(1)/(5)-(pi)/(4)}

tan[2.tan^(-1)(1/5)- pi/4]=

Evaluate the following: (i) tan{2\ tan^(-1)(1/5)-pi/4} (ii) tan(1/2\ sin^(-1)(3/4)

Evaluate: i) tan{1/2cos^(-1)sqrt(5)/3} , ii) tan{2tan^(-1)1/5-pi/4}

Evaluate tan{(-1)^(n)(pi)/(4)} where n is an integer

The value of tan(2tan^(-1)""(1)/(5)-(pi)/(4)) is

Evaluate: tan^(-1)((tan(5 pi))/(6))+cos^(-1){cos((13 pi)/(6))}