Inverse Trigonometric Functions · Class 12 · CBSE · Science Mathematics
Evaluate sin⁻¹(3/5) + sin⁻¹(4/5), and justify your answer using the principal-value ranges.
Practice question from Inverse Trigonometric Functions (Class 12 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.
medium · Subjective · Q-3BEDE4
Evaluate sin⁻¹(3/5) + sin⁻¹(4/5), and justify your answer using the principal-value ranges.
Answer: Let A = sin⁻¹(3/5) and B = sin⁻¹(4/5). Since A and B lie in [0, π/2], cos A = 4/5 and cos B = 3/5; hence sin(A + B) = (3/5)(3/5) + (4/5)(4/5) = 1. Also, A + B lies in [0, π], so A + B = π/2.
Solution
Let and . Both angles lie in , so and . Thus , and because , we obtain .
More from Inverse Trigonometric Functions
- Using the principal value of the inverse sine function, find sin⁻¹(−√3/2).
- For the function f(x) = cos⁻¹(2x − 1), which of the following gives its domain and range?
- Evaluate cos⁻¹(cos(7π/6)) using the principal value of cos⁻¹.
- Using the principal value of the inverse tangent function, find tan⁻¹(−√3).
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