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If X, Y, Z are the angles of a DeltaXYZ...

If X, Y, Z are the angles of a `DeltaXYZ` then prove that `cos^(2)""(X)/(2)+cos^(2)((Y+Z)/(2))=1`

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CALCUTTA BOOK HOUSE-TRIGONOMETRIC RATIOS OF COMPLEMENTARY ANGLES -EXERCISE
  1. If theta=0^(@) then the trigonometrical ratio tangent of complementary...

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

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  3. If 0^(@)angletheta angle20^(@), then find the value of theta when sin^...

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  4. If sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/(2), then then the value of (x...

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

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

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

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

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

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

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

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

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  13. If A+B=90^(@) then prove that tanA+tanB=(cosec^(2)A)/(sqrt(cosec^(2)A-...

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  14. Prove that tan4^(@)tan43^(@)tan47^(@)tan86^(@)=1.

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  15. If tanthetaxxtan3theta=1, then find the value of tan2theta.

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  16. If cos5theta=0, then find the value of costheta.

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  17. If 0ltxlt(pi)/(2) then prove that cos(sinx)gtsin(cosx)

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  18. Prove that (1)/(2sin10^(@))-2sin70^(@)=1.

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  19. Prove that tan70^(@)=2tan50^(@)+tan20^(@).

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  20. Prove that cos35^(@)42'cos24^(@)18'-cos54^(@)18'cos65^(@)42'=(1)/(2)

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