NCERT Class 12 · Ch 2 Miscellaneous Exercise · Q5
NCERT Class 12 Maths · Chapter 2 Inverse Trigonometric Functions · Miscellaneous Exercise Question 5
Prove cos⁻¹(4/5)+cos⁻¹(12/13)=cos⁻¹(33/65).
💡 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=cos⁻¹(4/5), β=cos⁻¹(12/13). Then sin α=3/5 and sin β=5/13.
- cos(α+β)=(4·12−3·5)/65=33/65.
- Both angles are acute, so 0<α+β<π, within the cosine-inverse range. Therefore cos⁻¹(33/65)=α+β.
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