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Given x^2=cos2theta Show that tan^-1((co...

Given `x^2=cos2theta` Show that `tan^-1((costheta+sintheta)/(costheta-sintheta))=pi/4+theta`

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BODY BOOKS PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. If y=(tan^(-1)x)^2, show that (x^2+1)^2y2+2x(x^2+1)y1=2 .

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  2. Given x^2=cos2theta Write down theta using the inverse of cosine.

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  3. Given x^2=cos2theta Show that tan^-1((costheta+sintheta)/(costheta-sin...

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  4. Given x^2=cos2theta Write tan^-1((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2...

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  5. tan^-1x+tan^-1(1/x)=.............

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  6. sin^-1(sintheta)=...............

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  7. Prove that sin^-1(2xsqrt(1-x^2))=2sin^-1x

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  8. Show that sin^-1(3/5)-cos^-1(12/13)=cosec^-1(65/16)

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  9. Write one branch of sin^-1x other than principal branch.

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  10. Write the simplest form of sin^-1[xsqrt(1-x)-sqrtx.sqrt(1-x^2)]

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  11. Prove that cosec^-1x+sec^-1x=pi/2

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  12. If cos^-1(x//a)+cos^-1(y//b)=alpha, Prove that x^2/a^2-(2xy)/(ab)cosal...

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  13. Find the value of sin^-1(-1/2)+cos^-1(-1/2)

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  14. The value of cos[2tan^(-1)(-7)] is :a)49/50 b)-49/50 c)24/25 d)-24/25

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  15. Find the value of sin^-1(sin((3pi)/4))

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  16. sin^-1sinx=x if and only if a)x in R b)x in [(-pi)/2,pi/2] c)x in [-1...

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  17. Consider the function f(x)=sin^(-1)(2xsqrt(1-x^2)),(-1)/sqrt2lexle1/sq...

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  18. tan^-1x+cot^-1x = a)0 b)pi/4 c)pi/2 d)pi

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  19. Show that tan^-1(1/8)+tan^-1(1/57)=tan^-1(1/7)

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  20. Prove that tan^-1(1/8)+2tan^-1(1/3)+tan^-1(1/57)=pi/4

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