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Prove the following identities: sin^6A+...

Prove the following identities: `sin^6A+cos^6A=1-3sin^2Acos^2A`

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Prove the following identities: sin^4A+cos^4A=1-2sin^2Acos^2A

Prove the following identities: cos^4A-cos^2A=sin^4A-sin^2A

Prove the following identities: sin^4A-cos^4A=sin^2A-cos^2A=2sin^2A-1=1-2cos^2A

Prove the following identities: (sin^2A)/(cos^2A)+(cos^2A)/(sin^2A)=1/(sin^2Acos^2A)-2

Prove the following identities : (sin A - cos A + 1)/(sin A + cos A - 1) = (cos A)/ (1 - sin A)

Prove the following identities : sin^(4) A - cos^(4) A = 2 sin^(2) A - 1

Prove the following identities : (sin A + cos A)/ (sin A - cos A) + (sin A - cos A)/ (sin A + cos A) = (2)/ (2 sin^(2) A - 1)

Prove the following identities: tan^2A-tan^2B=(cos^2B-cos^2A)/(cos^2Bcos^2A)=(sin^2A-sin^2B)/(cos^2Acos^2B) (sinA-sinB)/(cosA+cosB)+(cosA-cosB)/(sinA+sinB)=0

Prove the following identities: (sinA+cosA)/(sinA-cosA)+(sinA-cosA)/(sinA+cosA)=2/(sin^2A-cos^2A)=2/(2sin^2A-1)=2/(1-2cos^2A)

Prove the following identities: 2(sin^6theta+cos^6theta)-3(sin^4theta+cos^4theta)+1=0 sin^6theta+cos^6theta+3sin^2thetacos^2theta=1 (sin^8theta-cos^8theta)=(sin^2theta-cos^2theta)(1-2s in^2thetacos^2theta)

RD SHARMA ENGLISH-TRIGONOMETRIC IDENTITIES-All Questions
  1. Prove the following identities: sin^4A+cos^4A=1-2sin^2Acos^2A

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  2. Prove the following identities: sin^4A-cos^4A=sin^2A-cos^2A=2sin^2A-1...

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  3. Prove the following identities: sin^6A+cos^6A=1-3sin^2Acos^2A

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  4. Prove the following identities: sec^4A-sec^2A=tan^4A+tan^2A

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  5. Without using trigonometric tables, evaluate each of the following: (...

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  6. Without using trigonometric tables, evaluate each of the following: ...

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  7. Without using trigonometric tables, evaluate each of the following: (...

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  8. Without using trigonometric tables, evaluate each of the following: 2/...

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

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

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

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

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

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

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

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

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

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

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

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

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