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Find the general solution of the equatio...

Find the general solution of the equation `5cos^(2)theta+7sin^(2)theta-6=0`.

A

`(2n+1)(pi)/(4)`

B

`(2n-1)(pi)/(4)`

C

`(2n+3)(pi)/(4)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`5cos^(2)theta+7sin^(2)theta-6=0`
`rArr5cos^(2)theta+7(1-cos^(2)theta)-6=0`
`rArr5cos^(2)theta+7-7cos^(2)theta-6=0`
`rArr-2cos^(2)theta+1=0`
`rArr-(2cos^(2)theta-1)=0`
`rArrcos2theta=0" " [becausecos2theta=2cos^(2)theta-1]`
`rArrsintheta=(-21sqrt(4+16))/(8)`
`2theta=(2n+1)(pi)/(2)rArrtheta=(2n+1)(pi)/(4)`
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