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

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

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LHS=`sin^6theta+cos^6theta`
`=(sin^2theta)^3+(cos^2theta)^3`
Put `sin^2theta=a` and `cos^2theta=b`
LHS=`a^3+b^3`
...
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RD SHARMA-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. If tan theta +sin theta =m and tan theta -sin theta =n then prove m^2-...

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

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

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

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  7. Prove the following identity: (t a n A)/(1-cot A)+(cot A)/(1-t a n A)=...

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  8. Prove the following identity: (sin^3A+cos^3A)/(sinA+cosA)+(sin^3A-cos^...

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  9. Prove the following identity: (secA secB + tanA tanB)^2 - (secA tanB+ ...

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  10. Prove the following identity: (costheta)/(1-sintheta)=(1+costheta+sint...

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  11. Prove the following identity: (tan^3theta)/(1+tan^2theta)+(cot^3theta)...

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  12. If (ax)/(costheta)+(by)/(sintheta)=a^2-b^2 , and (axsintheta)/(cos^2th...

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  13. Prove the following identity: (1/(sec^2theta-cos^2theta)+1/(cos e c^2t...

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  14. Prove the following identity: (1+t a nalphat a nbeta)^2+(tanalpha-t a...

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  15. Prove the following identity: ((1+cottheta+t a ntheta)(sin theta-costh...

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  16. Prove the following identity: (2sinthetacostheta-costheta)/(1-sintheta...

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  17. Prove the following identity: costheta(t a ntheta+2)(2t a ntheta+1)=2s...

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  18. If sintheta=(a^2-b^2)/(a^2+b^2), find the value of t a ntheta,\ s e ct...

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  19. If t a ntheta=a/b ,\ show that (a\ sintheta-b costheta)/(\ a\ sinthet...

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  20. If cosectheta-sintheta=a^3, sectheta-costheta=b^3, then prove that a^...

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