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Prove that cosec^(2)22^(@)cot^(2)68^(@)=...

Prove that `cosec^(2)22^(@)cot^(2)68^(@)=sin^(2)22^(@)+sin^(2)68^(@)+cot^(2)68^(@)`.

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`cosec^(2)22^(@)cot^(2)68^(@)=cosec^(2)(90^(@)-68^(@))cot^(2)68^(@)`
`=sec^(2)68^(@)cot^(2)68^(@)=(1+tan^(2)68^(@))cot^(2)68^(@)`
`=cot^(2)68^(@)+tan^(2)68^(@)cot^(2)68^(@)`
`=cot^(2)68^(@)+tan^(2)68^(@)cot^(2)68^(@)`
`=cot^(2)68^(@)+tan^(2)68^(@).(1)/(tan^(2)68^(@))`
`=cot^(2)68^(@)+1`
`=cot^(2)68^(@)+sin^(2)22+cos^(2)(90^(@)-68^(@))`
`=cot^(2)68^(@)+sin^(2)22+sin^(2)68^(@)`
`=sin^(2)22^(@)+sin^(2)68^(@)+cot^(2)68^(@)`.
Hence `cosec^(2)22^(@)cot^(2)68^(@)=sin^(2)22^(@)+sin^(2)68^(@)+cot^(2)68^(@)`
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CALCUTTA BOOK HOUSE-TRIGONOMETRIC RATIOS OF COMPLEMENTARY ANGLES -EXERCISE
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  2. If A, B, C are the angles of a triangle then tan ((B+C)/2)=

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  5. If sec9theta=cosec9theta, then the value of theta is equal to

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  7. If sin(theta+36^(@))=costheta then the value of theta" is "27^(@)

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  8. The complementary angle of 90^(@) is

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  9. If in DeltaABC,angleC=90^(@) then 1+tan^(2)A

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  10. If theta=0^(@) then the trigonometrical ratio tangent of complementary...

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  11. Find the value of cos1^(@)cos2^(@)cos3^(@).............cos180^(@)

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  14. If X, Y, Z are the angles of a DeltaXYZ then prove that cos^(2)""(X)/...

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  15. If x=acos(90^(@)-theta)andy=bcot(90^(@)-theta), then prove that (a^(2)...

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  16. Prove that (1+sec22^(@)+cot68^(@))(1-cosec22^(@)+tan68^(@))=2

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  17. If angleA+angleB=90^(@) then prove that 1+(cotA)/(cotB)=cosec^(2)A

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  18. If alpha+beta=90^(@), then find the value of cotbeta+cosbeta-(cosbeta)...

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  19. Find the value of (5sin75^(@)sin77^(@)+2cos13^(@)cos15^(@))/(cos15^(@)...

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  20. If alpha+beta=90^(@) then prove that cosec^(2)alpha+cosec^(2)beta=cose...

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  21. Prove that sec^(2)11^(@)-(1)/(tan^(2)79^(@))=1.

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