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(1)/(2)cos ^(-1)""((5 cos x +3)/(5+3 cos...

`(1)/(2)cos ^(-1)""((5 cos x +3)/(5+3 cos x))= tan^(-1)""((1)/(2)tan ""(x)/(2))`

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Prove that ""(1)/(2)cos^(-1)""((5cos x+3)/(5+3 cos x))= tan^(-1)""((1)/(2)tan""(x)/(2))

cos ^(-1) ""((cos x + cos y)/(1+cos x cos y))= 2 tan ^(-1) (tan ""(x)/(2) tan ""(y)/(2))

Prove that, tan^(-1)((3 sin 2x)/(5+3 cos 2x))+tan^(-1)((1)/(4) tan x)=x .

Show that cos^(-1) ((cosx+cos y)/(1+cos x.cosy))= 2tan^(-1)(tan(x/2).tan(y/2)) .

cos^(-1)x= 2 sin ^(-1) sqrt((1-x)/(2))=2 cos ^(-1)""sqrt((1+x)/(2))=2tan^(-1)""(sqrt(1-x^(2)))/(1+x)

tan (cos ^(-1) x) = sin (cot ^(-1) ""(1)/(2))

Prove that tan^-1 ((3sin2x)/(5+3 cos2x)) + tan^-1(1/4 tanx = x .

If (1)/(2) sin^(-1) [(3 sin 2 theta)/(5 + 4 cos 2 theta)] = tan^(-1) x, " then " x =

2 tan ^(-1) (Cos x) = tan ^(-1) (2 "cosec"x)

3 sin ^(-1 ) ""(2x )/(1+x^(2))-4cos^(-1) ""(1-x^(2))/(1+x^(2))+2tan ^(-1)""(2x )/(1-x^(2))=(pi)/(3)

CHHAYA PUBLICATION-TRIGONOMETRIC INVERSE CIRCULAR FUNCTIONS-Long answer type questions
  1. tan ( 2 tan ^(-1)sqrt((1+cos theta)/(1-cos theta)))+ tan theta =0

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  2. tan ^(-1) ""{(sqrt(1+cos x)+sqrt(1-cos x)}/{sqrt(1+cosx)-sqrt(1-cos x)...

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  3. cos ^(-1) ""((cos x + cos y)/(1+cos x cos y))= 2 tan ^(-1) (tan ...

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  4. (1)/(2)cos ^(-1)""((5 cos x +3)/(5+3 cos x))= tan^(-1)""((1)/(2)tan "...

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

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  6. If cos ^(-1) x+ cos ^(-1) y= theta , show that x^(2)-2xycos thet...

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  7. If sin ( pi cos theta ) = cos (pi sin theta ), , then sho...

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  8. Prove that , a cos theta + b sin theta = sqrt(a^(2) +b^(2) ) cos ...

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  9. IF 2 cos 4 theta + 9 cos 2 theta -7=0 , then show that , theta ...

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  10. cot ^(-1)""x+cot^(-1)""2x=(3pi)/(4)

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  11. cot ^(-1)x+cot^(-1)(a^(2)-x+1)=cot ^(-1)(a-1)

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  12. tan ^(-1)""(1-x)/(1+x)""=(1)/(2) sin ^(-1)""(x)/(sqrt(1+x^(2)))

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  13. sin ^(-1) x+sin ^(-1) (1-x) = cos ^(-1) x

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  14. cos^(-1) ""(5)/(x)+cos^(-1) ""(12)/(x)=(pi)/(2)

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  15. 3 cot ^(-1)""(1)/(2-sqrt(3))+cot ^(-1)""x=(pi)/(2)

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  16. sin^(-1)x+sin ^(-1)""2x=(pi)/(3)

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  17. sin ^(-1)sqrt(3)x+sin ^(-1)x=(pi)/(2)

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  18. sin^(-1)x-sin ^(-1)y=(pi)/(3) and cos^(-1) x+ cos ^(-1) y=(2pi)/(3)

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  19. sin ^(-1)""(ax)/(C ) +sin ^(-1) ""(bx)/(c ) =sin ^(-1)""x where a^(2...

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  20. 2 tan ^(-1) (Cos x) = tan ^(-1) (2 "cosec"x)

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