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Prove that if two angles alphaandbeta ar...

Prove that if two angles `alphaandbeta` are complementary angles, then
`(secalpha)/(cosalpha)-cot^(2)beta=1`

Text Solution

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LHS `=(secalpha)/(cosalpha)-cot^(2)beta`
`=secalpha.(1)/(cosalpha)-cot^(2)(90^(@)-alpha)[:'alpha+beta=90^(@)]`
`=secalpha.secalpha-tan^(2)alpha=sec^(2)alpha-tan^(2)alpha=1`.
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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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  3. (sin21^(@)30')/(cos68^(@)30')

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  4. (sin52^(@)+cos38^(@))/(sin38^(@)+cos52^(@))

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

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  6. If the sum of any two acute angles be 180^(@), then they are called cm...

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

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

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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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