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If u=cot^(-1)sqrt(tanalpha)-tan^(-1)sqrt...

If `u=cot^(-1)sqrt(tanalpha)-tan^(-1)sqrt(tanalpha),t h e ntan(pi/4, u/2)i se q u a lto` (a)`sqrt(tanalpha)` (b) `sqrt(cotalpha)` (c)`tanalpha` (d) cot `alpha`

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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Evaluate : cos(2cos^(-1)x+sin^(-1)x)a tx=1/5

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

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

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

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  5. 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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  6. The domain of cos^(-1)(x^2-4) is

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

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

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

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

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

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

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

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

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

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

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  17. Prove that: sin{tan^(-1)((1-x^2)/(2x))+cos^(-1)((1-x^2)/(1+x^2))}=1

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  18. Find the principal values of (a) sin^(-1)((sqrt(3))/2) (b) sin^(-1)(...

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  19. Find the principal values of (a) sin^(-1)(1/2) (b) sin^(-1)(-1/(sqrt...

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  20. Find the value of sin^(-1)[cos{sin^(-1)(-(sqrt(3))/2)}] .

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