Class 12 Inverse Trigonometric Functions · Long Answer3 Marksinverse_trigonometric_identities
Class 12 Maths · Inverse Trigonometric Functions · Long Answer #93
Prove \(\cos[\sin^{-1}(3/5)+\cot^{-1}(3/2)]=6/(5\sqrt{13})\).
✅ Step-by-Step Solution
Final Answer: Identity proved.
- Let α=arcsin(3/5) and β=arccot(3/2), both acute.
- The ratios are sin α=3/5, cos α=4/5, sin β=2/√13 and cos β=3/√13.
- The addition formula gives cos(α+β)=(4·3−3·2)/(5√13).
- The value is 6/(5√13), as required.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Let α=arcsin(3/5) and β=arccot(3/2), both acute.
- [1 mark] The ratios are sin α=3/5, cos α=4/5, sin β=2/√13 and cos β=3/√13.
- [1 mark] The addition formula gives cos(α+β)=(4·3−3·2)/(5√13).
- [0.5 marks] The value is 6/(5√13), as required.
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