Home
Class 12
MATHS
If tan A=1//2, tan B=1//3, then prove th...

If `tan A=1//2, tan B=1//3`, then prove that `cos 2A=sin2B`.

Text Solution

Verified by Experts

`tan(A+B)=(tan A+tanB)/(1-tan A tanB)=((1)/(2)+(1)/(3))/(10(1)/(2)xx(1)/(3))=1`
`rArr A+B=45^(@)` (one of the possible values).
`therefore 2Agt90^(@)-2B`
`rArr cos 2A=sin2theta`
For value of A+B we get the same result.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.3|13 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.4|26 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.1|11 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

In a Delta ABC , If tan A/2, tan B/2, tan C/2 are in A.P. then cos A. cos B, cos C are in

If tan(A+B)=3 tan A , prove that (a) sin(2A+B)=2sin B

If triangleABC is a right triangle and if angleA=pi/2 , then prove that (i) cos^(2) B+cos^(2)C=1 (ii) sin^(2) B+sin^(2) C=1 cos B-cos C=-1+2 sqrt2 cos""B/2sin ""C/2

If tan (phi /2)= sqrt((1+a)/(1-a)) tan"" theta/2," then prove that cos "phi=(cos theta-a)/(1-a cos theta)

If tan beta=cos theta tan alpha , then prove that tan^(2)""(theta)/(2)=(sin(alpha-beta))/(sin(alpha+beta)) .

If cos(A-B)=3/5 and tan A tan B=2, then (a) cos A cos B=1/5 (b) sin A sin B=-2/5 (c) cos A cos B=-1/5 (d) sin A sin B=-1/5

If A + B + C = (pi)/(2) , prove that cos 2A + cos 2B + cos 2C = 1 + 4 sin A sin B cos C

If tan theta tan phi=sqrt((a-b)/(a+b)) , prove that a-bcos 2theta)(a-b cos 2phi) is independent of theta and phi .

If tan A = (1-cos B)//sinB , then tan 2A = tan B.