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If t a n^2theta=1-a^2 , prove that sect...

If `t a n^2theta=1-a^2` , prove that `sectheta+t a n^3thetacos e ctheta=(2-a^2)^(3//2).` Also, find the values of a for which the above result holds true.

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Given,
`sectheta+tan^3thetacosectheta`
`=sectheta[(sectheta+tan^3thetacosectheta)/(sectheta)]`
`=sectheta[1+tan^3theta⋅(costheta)/(sintheta)]`
`=sectheta[1+tan^3theta×cottheta]` ...
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  16. Prove the following identities: 2sec^2theta-sec^4theta-2cos e c^2theta...

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  17. Prove the following identities: (sintheta+cos e ctheta)^2+(costheta+s...

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  18. Prove the following identity: (1+cottheta-cos e ctheta)(1+t a ntheta+s...

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  19. Prove the following identity: (t a ntheta+s e ctheta-1)/(t a ntheta-s ...

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  20. If costheta+sintheta=sqrt(2)costheta, show that costheta-sintheta=sqrt...

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