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If sin(cos^(-1)(5/13)+sin^(-1)x)=1 find ...

If `sin(cos^(-1)(5/13)+sin^(-1)x)=1` find the value of `xdot`

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Given, `sin(cos^(-1)(5/13)+sin^(-1)x)=1`
=`(cos^(-1)(5/13)+sin^(-1)x)=sin^(-1)1`
=`cos^(-1)(5/13)+sin^(-1)x)=pi/2`
=`cos^(-1)(5/13)=pi/2-sin^(-1)x` ...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. If tan^(-1)x+tan^(-1)y=(4pi)/5, find cot^(-1)x+cot^(-1)ydot

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  2. If tan^(-1)x-cot^(-1)x=tan^(-1)""1/(sqrt(3)) find the value of xdot

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  3. If sin(cos^(-1)(5/13)+sin^(-1)x)=1 find the value of xdot

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  4. If cos(sin^(-1)(2/5)+cos^(-1)x)=0 find the value of xdot

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  5. Evaluate : cos(2cos^(-1)x+sin^(-1)x)a tx=1/5

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  6. Let f(x)=e^(cos^(-1){sin(x+pi/3)}) Then, f((8pi)/9)= (a)e^(5pi//18...

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  7. If u=cot^(-1)sqrt(tanalpha)-tan^(-1)sqrt(tanalpha),t h e ntan(pi/4- u/...

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  8. The number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin^...

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  9. If alpha=tan^(-1)(t a n(5pi)/4)a n dbeta=tan^(-1)(-tan(2pi)/3),t h e n...

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  10. The domain of cos^(-1)(x^2-4) is (a) [3,5] (b) [-1,1] (c)[-sqrt(5),-...

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  11. In a A B C , , if C is a right angle, then tan^(-1)(a/(b+c))+tan^(-1...

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  12. If 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x)/(...

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  13. Solve the following equations: sin[2cos^(-1)"{"cot"("2tan^(-1)x"}]...

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  14. Solve the equation of x:sin^(-1)x+sin^(-1)(1-x)=cos^(-1)x

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  15. cos(sin^-1 (3/5)+ cot^-1(3/2)) = 6/(5sqrt13)

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  16. Prove that : tan^(-1)((63)/(16))=sin^(-1)((5)/(13))+cos^(-1)((3)/(5))

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  17. Prove that: sin^(-1)((63)/(65))=sin^(-1)(5/(13))+cos^(-1)(3/5)

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  18. Solve the following equation for x : 3sin^(-1)(2x)/(1+x^2)-4cos^(-1)(...

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  19. Solve the following equation for x: tan^(-1)((2x)/(1-x^2))+cot^(-1)...

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  20. Solve for x : 2tan^(-1)(sinx)=tan^(-1)(2secx),\ x!=pi/2

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