NCERT Class 12 · Ch 2 Miscellaneous Exercise · Q7
NCERT Class 12 Maths · Chapter 2 Inverse Trigonometric Functions · Miscellaneous Exercise Question 7
Prove tan⁻¹(63/16)=sin⁻¹(5/13)+cos⁻¹(3/5).
💡 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(5/13), β=cos⁻¹(3/5), both acute. Then cos α=12/13, sin β=4/5.
- sin(α+β)=63/65 and cos(α+β)=16/65>0, so the sum is acute.
- Its tangent is 63/16. The principal arctangent therefore equals α+β.
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Prove cos⁻¹(12/13)+sin⁻¹(3/5)=sin⁻¹(56/65).
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