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Prove that : cos^(-1) (cos^(2)x - si...

Prove that :
`cos^(-1) (cos^(2)x - sin^(2)x) = 2x`

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MODERN PUBLICATION-INVERSE - TRIGONOMETRIC FUNCTIONS-EXERCISE 2 (b) (Short Answer Type Questions)
  1. Show that: tan(1/2sin^(-1)3/4)=(4\ sqrt(-7))/3

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  2. Prove that : tan^(-1) . 3/5 +tan^(-1). 1/4 = pi/4

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  3. Prove that : cos^(-1) (cos^(2)x - sin^(2)x) = 2x

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  4. Prove that: 3cos^(-1)x=cos^(-1)(4x^3-3x), x in [1/2,1]

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  5. Prove that : sin^(-1) (2x sqrt(1-x^(2)))= 2 sin^(-1) x, - 1/(sqrt(2...

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  6. Prove that : sin^(-1) (2x sqrt(1-x^(2)) ) = 2 sin^(-1) x , -1/(s...

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  7. Prove that : 2sin^(-1). ((2x )/(1+x^(2))), -1 le x lt 1

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  8. Prove that : tan^(-1)((2xsqrt(1-x^(2)))/(1-2x^(2))) =2sin^(- 1)x ...

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

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  10. Prove that tan^(-1) ((1-sqrt(x))/(1+sqrt(x))) = pi/4 - tan^(-1) sqr...

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  11. Evaluate sin^(-1) . 4/5 + sin^(-1) . 5/13 + sin^(-1) . 16/65

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  12. Prove that: sin^(-1)(12)/(13)+cos^(-1)4/5+tan^(-1)(63)/(16)=pi

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  13. Prove that : tan^(-1)1+tan^(-1)2+tan^(-1)3=pi

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  14. Prove that tan^(-1). 1/2 +tan^(-1). 2/11 = tan^(-1) . 3/4

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

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  16. Prove that 2tan^(-1) . 1/5 +tan^(-1). 1/4 = tan^(-1) . 32/43

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  17. Prove that 2 tan^(-1) . 1/5 +tan^(-1) . 1/6 = tan^(-1). 9/13

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  18. Prove that 2 tan^(-1) . 1/7 +tan^(-1) . 1/3 = tan^(-1) . 9/13

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  19. Prove that tan^(-1). 1/2 +tan^(-1). 1/5 = 1/2 cos^(-1). 16/65

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  20. Prove that: tan^-1(1/4)+tan^-1(2/9)=1/2 cos^-1(3/5).

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