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If 8 cos^2 theta+8 sec^2 theta=65 and 0^...

If `8 cos^2 theta+8 sec^2 theta=65` and `0^@` < `theta` <`pi/2`, then `4cos2 theta` is equal to

Text Solution

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`8cos^theta+8sec^2theta=65`
`Let cos^2theta=t`
`8t+8/t=65`
`8t^2-65t+8=0`
`8t(t-8)-1(t-8)=0`
`(8t-1)(t-8)`
`t=1/8,8`
`cos^2theta=1/8`
...
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