Class 12 Inverse Trigonometric Functions · Long Answer3 Marksinverse_trigonometric_equations
Class 12 Maths · Inverse Trigonometric Functions · Long Answer #99
Solve \(\cot^{-1}x+\tan^{-1}8=\pi/2\).
✅ Step-by-Step Solution
Final Answer: x=8
- Rearrange to arccot x=π/2−arctan8.
- The principal complementary identity gives π/2−arctan8=arccot8.
- Arccot is one-one on R, so arccot x=arccot8 implies x=8.
- Substitution verifies arccot8+arctan8=π/2; the unique solution is x=8.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Rearrange to arccot x=π/2−arctan8.
- [1 mark] The principal complementary identity gives π/2−arctan8=arccot8.
- [1 mark] Arccot is one-one on R, so arccot x=arccot8 implies x=8.
- [0.5 marks] Substitution verifies arccot8+arctan8=π/2; the unique solution is x=8.
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