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If x=a sec theta cosphi, y = b sec theta...

If `x=a sec theta cosphi, y = b sec theta sin phi and z=c tan theta`, then prove that
`(x^(2))/(a^(2))+(y^(2))/(b^(2))-(z^(2))/(c^(2))=1.`

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CALCUTTA BOOK HOUSE-TRIGONOMETRIC RATIOS AND TRIGONOMETRIC IDENTITIES -EXERCISE
  1. Prove that (sin A+sinB)/(cosB-cosA)=(cos A+cosB)/(sinA-sinB).

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  2. Prove that (sec theta-tan theta+1)/(sec theta+tan theta+1)=(1-sin the...

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  3. Prove that (1)/("cosec"alpha-cot alpha)-(1)/(sin alpha)=(1)/(sin alpha...

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  4. If "cosec" theta- sin theta=m^(3) and sec theta-cos theta=n^(3), then ...

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  5. eliminate theta : a(1) sec theta + b(1)tan theta+c(1)=0 , a(2)sec thet...

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  6. If tan theta=(a)/(b) , then find the value of (sin theta)/(cos^(8)thet...

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  7. If a^(2)sec^(2)alpha-b^(2)tan^(2)alpha=c^(2), then prove that sinalpha...

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  8. If tan theta=k, then show that sec theta+tan^(3)theta "cosec"theta=(1...

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  9. If tan^(2)theta=1-e^(2), then prove that sectheta+tan^(3)theta"cosec...

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  10. If " cosec"theta-sin theta=m and sec theta-cos theta=n, then prove tha...

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  11. If a sin x=b cosx=(2c tan x)/(1-tan^(2)x), then prove that (a^(2)-b^(...

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  12. If (sin alpha-cosalpha)/(sin alpha+cosalpha)=tan theta, then prove tha...

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  13. If (cos^(4)alpha)/(cos^(2)beta)+(sin^(4)alpha)/(sin^(2)beta)=1, then ...

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  14. If u(n)=sin^(n)alpha+cos^(n)alpha, then prove that 2u(6)-3u(4)+1=0.

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  15. If theta be a positive acute angle and tan theta=(a)/(b), then find th...

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  16. If tanA+sinA=m and tanA-sinA=n, then prove that m^(2)-n^(2)=4sqrt(mn)...

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  17. If k tan theta=tan k theta, then prove that (sin^(2)k theta)/(sin^(2)...

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  18. If c cos^(3)theta+3c cos theta sin^(2)theta=m and c sin^(3)theta+3c c...

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  19. If x=r cos theta cos phi, y=r cos theta sin phi, z=r sin theta, then p...

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  20. If x=a sec theta cosphi, y = b sec theta sin phi and z=c tan theta, th...

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