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Find the value of the expression sin[c...

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

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Verified by Experts

The correct Answer is:
`sqrt{frac{2}{3}}`
`sin [cot ^{-1}(cos frac{pi}{4})]=sin [cot ^{-1} frac{1}{sqrt{2}}] `
=`sin [sin ^{-1} sqrt{frac{2}{3}}] `

=`sqrt{frac{2}{3}}`
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Evaluate : cos(sin^(-1)(1/4)+sec^(-1)(4/3))

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

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

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  4. Prove that: sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3)=15 and tan^2(s...

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  5. Prove that: sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3)=15 and tan^2(sec...

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

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

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  8. If"sin"{cot^(-1)(x+1)}="cos"(tan^(-1)x), then find xdot

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  9. Solve the following equation for x : "cos"(tan^(-1)x)=sin(cot^(-1)...

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  10. Solve the following equation for x : "cos"(tan^(-1)x)=sin(cot^(-1)...

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  11. If x=cos e c[tan^(-1){"cos"(cot^(-1)(sec(sin^(-1)a)))}] and y="sec"[...

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  12. If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi , prove that: xsqrt(1-x^2)+ysqrt(1...

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  13. If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi, show that x^4+y^4+z^4+4x^2y^2z^2=...

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  14. If tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))}=alpha...

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  15. Prove that: tan{pi/4+1/2\ cos^(-1)(a/b)}+tan{pi/4-1/2\ cos^(-1)(a/b)}=...

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  16. Evaluate each of the following: sin(sin^(-1)(7/(25))) (ii) sin(cos^(...

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  17. Evaluate each of the following: sin(sec^(-1)(17)/8) (ii) "c o s e c...

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  18. Evaluate each of the following: (i)tan(cos^(-1)(8/(17))) (ii) cot(...

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  19. Prove the following results: tan(cos^(-1)4/5+tan^(-1)2/3)=(17)/6 (...

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  20. Prove the following results: tan(sin^(-1)(15)/(13)+cos^(-1)3/5)=(63...

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