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Prove that : 2sin^-1 (3/5) = tan^-1 (24/...

Prove that : `2sin^-1 (3/5) = tan^-1 (24/7)`

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Prove that : 2tan^-1 (1/5) + tan^-1 (7/17) = pi/4

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Prove that : 2tan^-1 (1/2) + tan^-1 (1/7) = tan^-1 (31/17)

Prove that : sin^-1 (3/5) + sin^-1 (5/13) = cos^-1 (33/65)

Prove that : 2 tan^-1 (1/2) + tan^-1 (1/5) =tan^-1 (23/11)

Prove that : 2tan^-1 (1/4) + tan^-1 (7/23) = pi/4

Prove that : 2tan^-1 (1/4) + tan^-1 (1/3) = tan^-1 (39/37)

Prove that : sin^-1 (-4/5) = cos^-1 (-3/5) - pi

Prove that : sin^-1 (3/5) + cos^-1 (5/sqrt26) =tan^-1 (19/17)

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PRADEEP PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. Find the value of cos^-1 ( cos 10)

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  2. Find the value of the following: tan^-1(tan(7pi/6))

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  3. Prove that : 2sin^-1 (3/5) = tan^-1 (24/7)

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  4. Prove that : sin^-1(8/17) + sin^-1(3/5) = sin^-1(77/85)

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  5. Prove that : cos^-1 (4/5) + cos^-1(12/13) = cos^-1 (33/65)

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  6. Prove that : cos^-1 (12/13) + sin^-1 (3/5) = sin^-1 (56/65)

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

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  8. Prove that : tan^-1(1/3) + tan^-1(1/5) + tan^-1(1/7) + tan^-1(1/8) = p...

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  9. Prove that tan^(-1)sqrtx = 1/2cos^(-1) ((1-x)/(1+x)), x in [0,1]

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  10. Prove that : cot^-1[(sqrt(1+sin x) + sqrt(1-sin x))/(sqrt1+sin x + sqr...

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  11. Prove that tan^-1((sqrt(1+x)- (sqrt(1-x)))/(sqrt(1+x) + (sqrt(1-x)))...

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  12. Prove that (9pi)/8 - 9/4 sin^-1 (1/3) = 9/4 si^-1 ((2sqrt2)/3)

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  13. Solve the 2 tan^-1 (cos x) = tan^-1 (2 cosec x).

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  14. Solve the following equations: tan^-1((1-x)/(1+x)) = 1/2 tan^-1 x, x...

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  15. sin(tan^-1x), |x|<1 is equal to :

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  16. If sin^-1(1-x) - 2sin^-1x = pi/2, then x is equal to :

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  17. tan^-1(x/y)-tan^-1((x-y)/(x+y)) is equal to :

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  18. Fill in the blanks: Domain of the function sin^-1 x is ……..

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  19. Range of function cos^-1 x is :

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  20. The principal value of tan^(-1)sqrt(3) is ............... .

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