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If `x` is any non-zero real number, show that `costheta' a n d ' sintheta` can never equal to `x+1/x ,`

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We know, Range of `cos theta` is `-1`,
. If `cos theta = x + 1/x`,
if `x > 1` then `1/x < 1`
Ultimately ` x + 1/x` > 1
which shows, `cos theta> 1` which is not possible
similarly sin theta is also not possible
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  5. If tantheta+sectheta=e^x then costheta equals

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  6. Prove that:sqrt((1-costheta)/(1+costheta))={cosectheta-cottheta,if 0 <...

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  10. Prove the following identities: 2sec^2theta-sec^4theta-2cos e c^2theta...

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

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

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

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

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  15. If acostheta+b sintheta=x and asintheta-bcostheta=y prove that a^2+...

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  16. If tan theta +sin theta =m and tan theta -sin theta =n then prove m^2-...

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  17. Prove the following identity: sec^4theta-sec^2theta=tan^4theta+tan^2th...

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  18. Prove that sin^6theta+cos^6theta=1-3sin^2thetacos^2theta

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  19. Prove the following identity: (cosec theta - sin theta)(sec theta-cos ...

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  20. Prove the following identity: cos e c\ theta(s e ctheta-1)-cottheta(1-...

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