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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.
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