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Prove the following trigonometric ide...

Prove the following trigonometric identities: `cos^2theta+1/(1+cot^2theta)=1` (ii) `1/(1+sintheta)+1/(1-sintheta)=2sec^2theta`

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RD SHARMA-TRIGONOMETRIC IDENTITIES-All Questions
  1. Without using trigonometric tables, evaluate each of the following: 2...

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  2. Prove the following trigonometric identities: (i)(1-sin^2theta)sec^2...

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  3. Prove the following trigonometric identities: cos^2theta+1/(1+cot^2...

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  4. Prove: cos e c^2theta+sec^2theta=cos e c^2thetasec^2theta

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  5. Prove the following trigonometric identities : cot^2theta-1/(sin^2t...

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  6. Prove the following trigonometric identities : (1+cot^2theta)(1-cos...

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  7. If x=rsinAcosC ,\ \ y=rsinAsinC and z=rcosA , prove that r^2=x^2+y^...

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  8. If acostheta+bsintheta=m and asintheta-bcostheta=n , prove that a^2...

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  9. If sintheta+sin^2theta=1 , prove that cos^2theta+cos^4theta=1

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  10. If sectheta+tantheta=p , obtain the values of sectheta,tantheta and s...

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  11. Prove the following identities: (i)costhetasin(90^o-theta)+sinthetac...

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  12. Prove: (1-cos^2A)cos e c^2A=1

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  13. Prove: (1+cot^2A)sin^2A=1

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  14. Prove: tan^2thetacos^2theta=1-cos^2theta

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  15. Prove: cos e c\ thetasqrt(1-cos^2theta)=1

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  16. Prove: (sec^2theta-1)(cos e c^2theta-1)=1

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  17. Prove: tantheta+1/(tantheta)=sectheta\ cos e c\ theta

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  18. Prove: (costheta)/(1-sintheta)=(1+sintheta)/(costheta)

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  19. Prove: (costheta)/(1+sintheta)=(1-sintheta)/(costheta)

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  20. Prove: cos^2A+1/(1+cot^2A)=1

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