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If sinalpha=x and tan alpha=y, prove tha...

If `sinalpha=x and tan alpha=y,` prove that, `1/x^2-1/y^2=1`.

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CHHAYA PUBLICATION-TRIGONOMETRIC RATIOS [OR FUNCTIONS] OF POSITIVE ACUTE ANGLES-EXERCISE 2
  1. Express 1+4cosec^2alphacot^2alpha in the form of a perfect square.

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  2. If 3cos alpha-4sinalpha=5, show that, 3sinalpha+4cosalpha=0 .

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  3. If sinalpha=x and tan alpha=y, prove that, 1/x^2-1/y^2=1.

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  4. If tan alpha+cotalpha=2, show that, tan^7alpha+cot^7alpha=2.

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  5. If an=sin^n theta+cosec^ntheta and a1=2 prove that, an=2 .

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  6. If cosalpha+secalpha=2, show that cos^3alpha+sec^3alpha=2.

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  7. If x=rcos thetacosphi,y=rcosthetasinphi and z=r sin theta, show that ,...

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  8. If x=asec thetacosphi,y=bsec thetasin phi and z=ctantheta, show that, ...

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  9. If x=cosec theta -sin theta and y=sec theta-cos theta, then show that ...

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  10. Prove the following identities: (sec theta-tan theta+1)/(sec theta+t...

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  11. Prove the following identities: (sin theta-cos theta+1)/(sin theta+co...

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  12. Prove the following identities: 1/(secA-tanA)-1/(cosA)=1/(cosA)-1/(s...

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  13. Prove the following identities: (1-sin alpha+cosalpha)^2=2(1+cos alp...

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  14. Prove the following identities: cos^8A-sin^8A=(1-2sin^2Acos^2A)(1-2s...

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  15. Prove the following identities: sqrt((1-cos theta)/(1+cos theta))-co...

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  16. Prove the following identities: cot^2alpha(secalpha-1)/(1+sinalpha)+...

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  17. Prove the following identities: (cos alpha cos beta+sin alphasin bet...

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  18. Solve : (0^@le thetale90^@): tan theta +cot theta=2

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  19. Solve : (0^@le thetale90^@): 2cos^2 theta +5 sin theta =4

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  20. Solve : (0^@le thetale90^@): tan^2 theta-(sqrt(3)+1) tan theta+sqrt...

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