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If A+B=90^(@) then prove that 1+(tanA)/(...

If `A+B=90^(@)` then prove that `1+(tanA)/(tanB)=sec^(2)A.`

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`A+B=90^(@)impliesB=90^(@)-A`
`:.1+(tanA)/(tanB)=1+(tanA)/(tan(90^(@)-A))`
`=1+(tanA)/(cotA)=1+tanA.tanA`
`=1+tan^(2)A=sec^(2)A`.
Hence `1+(tanA)/(tanB)=sec^(2)A.`
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CALCUTTA BOOK HOUSE-TRIGONOMETRIC RATIOS OF COMPLEMENTARY ANGLES -EXERCISE
  1. If A+B=90^(@) then prove that 1+(tanA)/(tanB)=sec^(2)A.

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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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