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Prove that : 2tan^(-1)[tan prop//2 tan b...

Prove that : `2tan^(-1)[tan prop//2 tan beta//2]=cos^(-1)[(cos prop +cosbeta)/(1+cosalpha cos beta)]`

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CBSE COMPLEMENTARY MATERIAL-INVERSE TRIGONOMETRIC FUNCTIONS-4 MARK QUESTIONS
  1. Prove that tan^(-1)((a-b)/(1+ab))+ tan^(-1)((b-c)/(1+bc))+tan^(-1)((c-...

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  2. Q. if tan^-1 a+tan^-1 b+tan^-1 c=pi, then prove that a+b+c=abc.

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  3. If cos^(-1)x+cos^(-1)y+cos^(-1)=pi,p rov et h a tx^2+y^2+z^2+2x y z=1.

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  4. if tan^-1(1/(1+1*2))+tan^-1(1/(1+2*3))+.............+tan^-1(1/(1+n*(n+...

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  5. If (tan^(-1)x)^2+(cot^(-1)x)^2=(5pi^2)/8, then find xdot

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

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  7. Solve the equation sin^(-1)y x+sin^(-1)6sqrt(3)x=(-pi)/2dot

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  8. If sin^(-1)x+sin^(-1)(1-x)=cos^(-1)x then x equals

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  9. Solve sin^(-1) (5/x) + sin^(-1)(12/x) = pi/2

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  10. Solve the following for x sin^(-1)((x)/(2))+cos^(-1)x=(pi)/(6)

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  11. If cos^(-1)(x/2)+cos^(-1)(y/3) = theta, prove that 9x^2- 12xycostheta+...

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  12. Prove that: tan^(-1)[(3 sin 2 phi)/(5+3cos 2phi)]+tan^(-1)[(1)/(4) tan...

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  13. The value of sin^(-1){cot(sin^(-1)(sqrt((2-sqrt3)/4)+cos^(-1)(sqrt(12)...

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  14. prove that 2tan^-1(sqrt((a-b)/(a+b))tan(theta/2))=cos^-1((acostheta+b)...

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  15. Prove that : 2tan^(-1)[tan prop//2 tan beta//2]=cos^(-1)[(cos prop +co...

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  16. tan((pi)/(4) +(1)/(2)"cos"^(-1)(a)/(b))+ tan((pi)/(4) - (1)/(2)"cos"^(...

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  17. Prove that : cot^(-1)7+cot^(-1)8+cot^(-1)18=cot^(-1)3

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  18. Show taht 2tan^-1(tan(alpha/2)tan(pi/4-beta/2))=tan^-1((sinalphacosbet...

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  19. Solve: tan^(-1)(x-1)/(x+1)+tan^(-1)(2x-1)/(2x+1)=tan^(-1)(23)/(36)

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  20. Solve tan^-1(1/(1+2x))+tan^-1(1/(1+4x))=tan^-1(2/x^2)

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