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Prove that cos^-1 ((sin x + cos x )/(sqr...

Prove that `cos^-1 ((sin x + cos x )/(sqrt2)) = x - (pi/4), (pi/4) le x le ((5pi)/4)`

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PRADEEP PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. Prove that cos^-1 ((sin x + cos x )/(sqrt2)) = x - (pi/4), (pi/4) le x...

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

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  3. Find the principal value of sin^-1(1/sqrt2)

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  4. Find the value of sin^-1(-1)

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  5. Find the value of sin^-1(-(1/2))

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  6. Find the principal value of cos^-1(sqrt3/2)

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  7. Find the value of cos^-1(-sqrt3/2)

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  8. Find the value of cos^-1(-1)

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  9. Find the principal value ofcos^-1(-1/sqrt2)

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  10. Find the value of sin(sin^-1 x + cos^-1 x ), |x| le 1

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  11. Find the value of sin^-1(sin(0pi/10))

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  12. Find the value of cos^-1(sqrt3/2) + 2 sin^-1(sqrt3/2)

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  13. Find the value of sin^-1[cos(sin^-1(sqrt3/2))]

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  14. Prove that following : 2 sin^-1 x = cos^-1 (1-2x^2), 0 le x le 1

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  15. Prove the following: 3sin^–1 x = sin^–1 (3x – 4x^3), x in [–1/2 , 1/2]

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  16. Prove the following: 3cos^–1 x = cos^–1 (4x^3 – 3x), x in [1/2,1]

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  17. Prove that following : cos^-1 x = 2 sin^-1 sqrt(1-x)/(2) = 2cos^-1 s...

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  18. Prove that following : sin(2 cos^-1(-4/5)) = - (24/25)

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  19. Prove that following : cos(2sin^-1(-2/5)) = 17/25

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  20. Prove that following : cos(3cos^-1(2/5)) = - (118)/(125)

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  21. Write the following functions in the simplest form: sin^-1 sqrt(1-x^...

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