Home
Class 12
MATHS
If theta=pi/(4n) then the value of tanth...

If `theta=pi/(4n)` then the value of `tanthetatan(2theta)tan(3theta)....tan((2n-1)theta)` is

Text Solution

Verified by Experts

The correct Answer is:
1
`2n theta=pi//2`
`:. theta,(2n-1)theta=(pi//2)-theta`
`or 2theta,(2n-2)theta=(pi//2)-2theta,...`
They form complementary angles A and B so that `tanA tanB=tanAcotA=1` for each pair.
Also, `tanntheta=tan. Pi/4=1`
Hence, the value of product is 1
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Single)|57 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|17 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 2.5|16 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Archives (Matrix Match Type)|1 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Matrix Match Type|1 Videos

Similar Questions

Explore conceptually related problems

If theta_1,theta_2,theta_3 are the three values of thetain[0,2pi] for which tantheta=lambda then the value of tan(theta_1)/3tan(theta_2)/3+tan(theta_2)/3tan(theta_3)/3+tan(theta_3)/3tan(theta_1)/3 is equal to

Solve tantheta+tan2theta+sqrt(3)tanthetatan2theta=sqrt(3)

(sec theta+ tan theta)(sec theta-tan theta) =____.

Solve tan theta+tan 2 theta+sqrt(3) tan theta tan 2 theta = sqrt(3) .

The general solution of tan theta+tan 2 theta+tan 3 theta=0 is

Prove that tan^2 (theta)-sin^2 (theta)= tan^2 (theta) sin^2 (theta)

If tan6theta=p/q , find the value of 1/2(pcosec2theta-qsec2theta)

Solve 4 cos theta-3 sec theta=tan theta .

If sec theta = x + (1)/(4x) , then sec theta + tan theta =

Prove that (tan^(2)2theta-tan^(2)theta)/(1-tan^(2)2thetatan^(2)theta)=tan 3 theta tan theta .