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If costheta+sintheta=sqrt(2)costheta, sh...

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

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RD SHARMA ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. Prove the following identity: (1+cottheta-cos e ctheta)(1+t a ntheta+s...

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

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

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

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

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

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

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  8. Prove the following identity: (cosectheta-sintheta)(s e ctheta-costhet...

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

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  10. Prove the following identity: (1-sin AcosA)/(cos A(s e c A-cosec A))do...

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

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

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  13. Prove the following identity: (s e c A\ s e c B+t a n AtanB)^2-(s e c ...

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

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

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

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

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

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  19. Prove the following identity: ((1+cottheta+t a ntheta)(sintheta-costhe...

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

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