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If sin^(-1) x = pi//5, for some x in (-1...

If `sin^(-1) x = pi//5`, for some `x in (-1, 1)`, then find the value of `cos^(-1) x`

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To solve the problem, we start with the given equation: 1. **Given**: \[ \sin^{-1} x = \frac{\pi}{5} \] 2. **Using the identity**: ...
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CENGAGE ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS-Illustration
  1. The value of 2 tan^(-1) (cosec tan^(-1) x - tan cot^(-1) x) is equal t...

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  2. Prove that cos (tan^(-1) (sin (cot^(-1) x))) = sqrt((x^(2) + 1)/(x^(2)...

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  3. If sin^(-1) x = pi//5, for some x in (-1, 1), then find the value of c...

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  4. If sin (sin^(-1).(1)/(5) + cos^(-1) x) = 1, then find the value of x

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  5. solve sin^(-1) x le cos^(-1) x

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  6. Find the range of f(x) = sin^(-1) x + tan^(-1) x + cos^(-1) x

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  7. Find the minimum value of (sec^(-1) x)^(2) + (cosec^(-1) x)^(2)

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  8. Find the range of f(x) = (sin^(-1) x)^(2) + 2pi cos^(-1) x + pi^(2)

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  9. Solve sin^(-1). (14)/(|x|) + sin^(-1).(2 sqrt15)/(|x|) = (pi)/(2)

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  10. If alpha = sin^(-1) (cos(sin^-1) x)) and beta = cos^(-1) (sin (cos^(-1...

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  11. If sec^(-1) x = cosec^(-1) y, then find the value of cos^(-1).(1)/(x) ...

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  12. Prove that tan^(-1) x + tan^(-1).(1)/(x) = {(pi//2,"if" x gt 0),(-pi//...

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  13. For which values of x, function f(x) = sin^(-1) x + sin^(-1).(1)/(x) +...

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  14. Find the value of sum(r = 1)^(10) sum(s = 1)^(10) tan^(-1) ((r)/(s))

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  15. If sin^(-1)xi in [0,1]AAi=1,2,3, .28 then find the maximum value of s...

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  16. If two angles of a triangle are tan^(-1) (2) and tan^(-1) (3), then fi...

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

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  18. Prove that: tan^(-1)(1/2tan2A)+tan^(-1)(cota)+tan^(-1)(cot^3A)={ when ...

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  19. Let a, b and c be positive real numbers. Then prove that tan^(-1) sqrt...

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  20. Simplify [(3 sin 2 alpha)/(5 + 3 cos 2 alpha)] + tan^(-1) [(tan alph...

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