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sin⁻1 (cos(sin⁻1 x) + cos⁻1 (sin(cos⁻1 x) is equal to
  • a)
    0
  • b)
    π/4
  • c)
    π/2
  • d)
    3π/4
Correct answer is option 'C'. Can you explain this answer?
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Explanation:

Given equation:
sin1 (cos(sin1x) + cos1 (sin(cos1 x)

Using trigonometric identities:
- sin(90° - x) = cos(x)
- cos(90° - x) = sin(x)

Substituting the identities:
sin(90° - sin(x)) + cos(90° - cos(x))

Expanding the equation:
sin(90°)cos(x) - cos(90°)sin(x) + cos(90°)sin(x) + sin(90°)cos(x)

Solving the trigonometric functions:
cos(x) - sin(x) + sin(x) + cos(x)
2cos(x)

When x = π/2:
2cos(π/2) = 2*0 = 0

Therefore, the given expression is equal to 0. Hence, the correct answer is (a) 0.
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sin⁻1 (cos(sin⁻1x) + cos⁻1 (sin(cos⁻1 x) is equal toa)0b)π/4c)π/2d)3π/4Correct answer is option 'C'. Can you explain this answer?
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