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If xcostheta-ysintheta=a and xsintheta+y...

If x`costheta-ysintheta=a` and `xsintheta+ycostheta=b` , then prove that `x^2+y^2=a^2+b^2` .

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MBD-INTRODUCTION TO TRIGONOMETRY-EXERCISE
  1. Prove that (cosectheta+cottheta)(1-costheta)=sintheta .

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

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

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

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

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

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

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

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

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  10. Prove that (1-costheta)/(1+costheta)=(cosectheta-cottheta)^2 .

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  11. sqrt(sec^2theta+cosec^2theta)=tantheta+cottheta=sectheta.cosectheta. .

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  12. Prove that sqrt((1+sinA)/(1-sinA))=(1+sinA)/cosA .

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  13. Prove that sqrt((1+costheta)/(1-costheta))=cosectheta+cottheta .

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  14. Prove that sqrt((sectheta-tantheta)/(sectheta+tantheta))=sectheta-tant...

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  15. sqrt((cosectheta+1)/(cosectheta-1))=costheta/(1-sintheta)=(cottheta)/(...

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  16. Prove that (tan^3theta-1)/(tantheta-1)=sec^2theta+tantheta .

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  17. Prove that 1/(1+sintheta)+1/(1-sintheta)=2sec^2theta .

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  18. Prove that sintheta/(1+costheta)+sintheta/(1-costheta)=2/sintheta .

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  19. (sinA-sinB)/(cosA+cosB)+(cosA-cosB)/(sinA+sinB)=0 .

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  20. If xcostheta-ysintheta=a and xsintheta+ycostheta=b , then prove that x...

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