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Evaluate: sin(cos^(-1)3/5+cos e c^(-1)(1...

Evaluate: `sin(cos^(-1)3/5+cos e c^(-1)(13)/5)`

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To evaluate the expression \( \sin(\cos^{-1} \frac{3}{5} + \cos^{-1} \frac{13}{5}) \), we can use the sine addition formula: \[ \sin(A + B) = \sin A \cos B + \cos A \sin B \] where \( A = \cos^{-1} \frac{3}{5} \) and \( B = \cos^{-1} \frac{13}{5} \). ...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Prove that: sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3)=15 and tan^2(s...

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  2. Prove that: "sin"[cot^(-1){"cos"(tan^(-1)x)}]=sqrt((x^2+1)/(x^2+2)) ...

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  3. Evaluate: sin(cos^(-1)3/5+cos e c^(-1)(13)/5)

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  4. Find the value of the expression sin[cot^(-1){cos(tan^-1 1)}]

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  5. Write the value of sin{pi/3-sin^(-1)(-1/2)}

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  6. If tan^(-1)x+tan^(-1)y=pi/4, then write the value of x+y+x ydot

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  7. Prove that 2tan^(-1)(sqrt((a-b)/(a+b))tan(theta/2))=cos^(-1)((acosthet...

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  8. Solve the following equation for x : tan^(-1)(1/4)+2tan^(-1)(1/5)+...

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  9. Write the value of cos^2(1/2cos^(-1)3/5)

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

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

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

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

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

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

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

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

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

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

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  20. Evaluate each of the following: sin^(-1)(s inpi/3) (ii) cos^(-1)(cos(...

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