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Prove that: tan^(-1){(cos2alphasec2beta...

Prove that: `tan^(-1){(cos2alphasec2beta+cos2betasec2alpha)/2}=tan^(-1){tan^2(alpha+beta)tan^2(alpha-beta)}+tan^(-1)1`

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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Write the value of cos^2(1/2cos^(-1)3/5)

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  2. Write the value of sin^-1(sin1550^@)

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  3. Prove that: tan^(-1){(cos2alphasec2beta+cos2betasec2alpha)/2}=tan^(-1...

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  4. Prove that: (alpha^3)/2cos e c^2(1/2tan^(-1)alpha/beta)+(beta^3)/2sec^...

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  5. Show that :2tan^(-1)x+sin^(-1)(2x)/(1+x^2) is constant for xgeq1, find...

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  6. Prove that: tan^(-1)((1-x^2)/(2x))+cot^(-1)((1-x^2)/(2x))=pi/2

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  7. Simplify each of the following: cos^(-1)(3/5cosx+4/5sinx) , where -(...

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  8. Write the following functions in the simplest form: tan^(-1){x/(sqrt...

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  9. Evaluate each of the following: cot^(-1)(1/(sqrt(3)))-cos e c^(-1)(-2)...

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  10. For the principal values, evaluate the following: cot^(-1)(-1)+cos e ...

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  11. Prove that: (i)tan^(-1){(sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqr...

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  12. Evaluate each of the following: sin^(-1)(sinpi/3) (ii) cos^(-1)(cos(2...

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  13. If cos e c^(-1)x+cos e c^(-1)y+cos e c^(-1)z=-(3pi)/2, find the value ...

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  14. For the principal values, evaluate the following: tan^(-1)sqrt(3)-se...

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  15. Find the principal values of cot^(-1)sqrt(3) and cot^(-1)(-1)

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  16. For the principal values, evaluate the following: sin^(-1)(-(sqrt(3))...

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  17. The value of tan{cos^(-1)1/(5sqrt(2))-sin^(-1)4/(sqrt(17))} is (sqrt(2...

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  18. sin(cot^(-1)(tan(cos^(-1)x))) is equal to a) x b) sqrt(1-x^2) c) 1/x d...

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  19. Write the value of tan^(-1){2sin(2cos^(-1)(sqrt(3))/2)}dot

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  20. Write the principal value of cos^(-1)(cos680^0)dot

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