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Prove that sin^4theta+cos^4theta=1-2sin^...

Prove that `sin^4theta+cos^4theta=1-2sin^2thetacos^2theta` .

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Prove that sin^4theta-cos^4theta=sin^2theta-cos^2theta .

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Prove the following identity : sin^4 theta+ cos^4 theta= 1-2 sin^2 theta cos^2 theta .

Prove that : sin^8 theta- cos^8 theta= (sin^2 theta- cos^2 theta)(1-2 sin^2 theta cos^2 theta) .

Prove the following identity : cos^4 theta- sin^4 theta= cos^2 theta-sin^2 theta= 2 cos^2 theta-1=1-2 sin^2 theta .

Prove the following identity : sin^6 theta+ cos^6 theta= 1-3 sin^2 theta cos^2 theta .

If theta be any real, prove that : cos4 theta=1-8 sin^2 theta cos^2 theta =1-8 cos^2 theta +8 cos^4 theta .

Prove that (sin theta-cos theta+1)/(sin theta+cos theta-1)=1/(sec theta-tan theta) ,using the identity sec^2 theta=1+tan^2 theta .

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MBD-INTRODUCTION TO TRIGONOMETRY-EXERCISE
  1. Prove that (1 +cottheta-cosectheta)(1+tantheta+sectheta)=2.

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  2. Prove that (sintheta)/(cottheta+cosectheta)=2+sintheta/(cottheta-cosec...

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  3. Prove that sin^4theta+cos^4theta=1-2sin^2thetacos^2theta .

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  4. Prove that sin^4theta-cos^4theta=sin^2theta-cos^2theta .

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  5. Prove that sintheta(cosectheta-sintheta)=cos^2theta .

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  6. Prove that cottheta+tantheta=secthetacosectheta .

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  7. Prove that (cosA+sinA)^2+(cosA-sinA)^2=2 .

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  8. Prove that tan^2theta-sin^2theta=tan^2thetasin^2theta .

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  9. Prove that sec^4theta-sec^2theta=tan^4theta+tan^2theta .

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  10. Prove that (1+tan^2theta)sinthetacostheta=tantheta .

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  11. Prove that (sectheta+tantheta)(1-sintheta)=costheta .

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  12. Prove that (cosectheta+cottheta)(1-costheta)=sintheta .

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  13. Prove that sin^3theta+cos^3theta=(sintheta+costheta)(1-sinthetacosthet...

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

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  15. Prove that 1/(cosecA+cotA)=(cosecA-cotA) .

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  16. Prove that (cosecA+cotA)/(cosecA-cotA)=(cosecA+cotA)^2 .

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  17. Prove that (cosecA)/(cosecA-1)+(cosecA)/(cosecA+1)=2sec^2A .

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  18. Prove that (sec^2theta-sin^2theta)/tan^2theta=cosec^2theta-cos^2theta ...

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  19. Prove that:(1+cos^2A)/(sin^2A)=2cosec^2A-1

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  20. Prove that (1/costheta-costheta)(1/sintheta-sintheta)=1/(tantheta+cott...

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