NCERT Class 12 · Ch 2 Miscellaneous Exercise · Q3
NCERT Class 12 Maths · Chapter 2 Inverse Trigonometric Functions · Miscellaneous Exercise Question 3
Prove 2sin⁻¹(3/5)=tan⁻¹(24/7).
💡 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: Both sides equal the same acute angle.
- Let θ=sin⁻¹(3/5). Then cos θ=4/5 and 0<θ<π/4 because 3/5<1/√2.
- tan 2θ=2(3/4)/(1−9/16)=24/7.
- Since 0<2θ<π/2, principal tan⁻¹(24/7)=2θ.
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