Class 12 Inverse Trigonometric Functions · Long Answer3 Marksinverse_trigonometric_identities
Class 12 Maths · Inverse Trigonometric Functions · Long Answer #64
Evaluate \(\sin[\cos^{-1}(4/5)+\tan^{-1}(2/3)]\).
✅ Step-by-Step Solution
Final Answer: 17/(5√13)
- Let α=arccos(4/5), β=arctan(2/3); both angles are acute.
- Their ratios are sin α=3/5, cos α=4/5, sin β=2/√13, cos β=3/√13.
- Use sin(α+β)=sin α cos β+cos α sin β=(3·3+4·2)/(5√13).
- The value is 17/(5√13).
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Let α=arccos(4/5), β=arctan(2/3); both angles are acute.
- [1 mark] Their ratios are sin α=3/5, cos α=4/5, sin β=2/√13, cos β=3/√13.
- [1 mark] Use sin(α+β)=sin α cos β+cos α sin β=(3·3+4·2)/(5√13).
- [0.5 marks] The value is 17/(5√13).
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