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Prove that tan^(-1)((cosx)/(1+sinx))=(pi...

Prove that `tan^(-1)((cosx)/(1+sinx))=(pi/4-x/2)`

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Verified by Experts

We have,
LHS `=tan^(-1)(cosx)/(1+sinx)`
`=tan^(-1){(sin(pi/2-x))/(1+cos(pi/2-x))}`
`=tan^(-1){(2sin(pi/4-x/2)cos(pi/4-x/2))/(2cos^(2)(pi/4-x/2))}`
`=tan^(-1){tan(pi/4-x/2)}=(pi/4-x/2)`=RHS.
`therefore tan^(-1)((cosx)/(1+sinx))=(pi/4-x/2)`.
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RS AGGARWAL-INVERSE TRIGNOMETRIC FUNCTIONS -Objective Questons
  1. Prove that tan^(-1)((cosx)/(1+sinx))=(pi/4-x/2)

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  2. Find the principal value of: cos^(-1)((sqrt(3))/2)

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  3. Find the principal value of the following: (i) cosec^(-1)(2) (ii) ta...

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  4. Find the principal value of: cos^(-1)(-1/(sqrt(2)))

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  5. Find the principal value of: sin^(-1)(-1/2)

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  6. The principal value of cos^(-1)(-1/2) is

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  7. The principal value of tan^-1(-sqrt3) is

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  8. The principal value of cot^(-1)(-1) is

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  9. Find the principal value of sec^(-1)((-2)/(sqrt(3)))

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  10. The principal value of "cosec"^(-1)(-sqrt(2)) is

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  11. Find the principal values of each of the following: cot^(-1)(-sqrt(...

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  12. The principle value of sin ^(-1)(sin ""(2pi)/(3)) is

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  13. The value of cos^(-1)(cos(14pi/6)) is

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  14. The value of tan^(-1)(tan(8*pi/6)) is

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  15. Find the value of : cot^(-1), (5pi/4)

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  16. The value of sec^(-1)(sec(8pi)/5) is

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  17. The value of "cosec"^(-1)("cosec"(4pi)/3) is

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  18. प्रश्न संख्या 16 से 18में दिए प्रत्येक व्यंजन का मान ज्ञात कीजिए : t...

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  19. pi/3-sin^(-1)(-1/2)=?

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  20. The value of sin(sin^(-1)(1/2)+cos^(-1)(1/2))=?

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  21. If x ne 0 then cos(tan^(-1)+cot^(-1)x)=?

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