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If sin A + sin 2A = x and cos A + cos 2A...

If sin A + sin 2A = x and cos A + cos 2A = y, then `(x^(2)+y^(2)) (x^(2)+y^(2)-1)=`

A

2y

B

y

C

3y

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Squaring and adding, we get
`x^(2)+y^(2)=1+1+2 cos (2A-A)`
`therefore (x^(2)+y^(2)-2)/(2)=cos A` ….(1)
Also `cos A + 2 cos^(2)A-1=y`
or `(cos A+1)(2cos A-1)=y`
Put value of cos A from (1) and and get the answer.
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