If `8 cos^2 theta+8 sec^2 theta=65` and `0^@` < `theta` – InterviewSolution

InterviewSolution

1.	If `8 cos^2 theta+8 sec^2 theta=65` and `0^@` < `theta`
Answer» `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` `costheta=1/(2sqrt2)` `4cos2theta=4(2cos^2theta-1)` `=4(2*1/8-1)` `=-3`.

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