NCERT Class 12 · Ch 2 Miscellaneous Exercise · Q4
NCERT Class 12 Maths · Chapter 2 Inverse Trigonometric Functions · Miscellaneous Exercise Question 4
Prove sin⁻¹(8/17)+sin⁻¹(3/5)=tan⁻¹(77/36).
💡 Concept Hints
- Recall the principal range of the inverse function before simplifying.
- Find an angle with the required trigonometric value, then verify it belongs to the principal range.
✅ Step-by-Step Solution
Final Answer: The identity holds.
- Let α=sin⁻¹(8/17), β=sin⁻¹(3/5). Both are acute; cos α=15/17, cos β=4/5.
- sin(α+β)=(32+45)/85=77/85; cos(α+β)=(60−24)/85=36/85.
- The sum lies in (0,π), and its positive cosine puts it in (0,π/2). Its tangent is 77/36, so the principal arctangent equals α+β.
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