CBSE Class 12 Mathematics 2026 Main Paper 65/1/2 · Q252 Marksprincipal_values
CBSE Class 12 Mathematics 2026 Main Paper 65/1/2 · Question 25 (Inverse Trigonometric Functions)
Simplify \(\cot^{-1}\sqrt{(1+\cos 2x)/(1-\cos 2x)}\) for \(0<x<\pi/2\). OR Evaluate \(\sin(\tan^{-1}(-\sqrt3)-\sec^{-1}2)\).
Alternative 1 2 Marks
Simplify \(\cot^{-1}\sqrt{(1+\cos 2x)/(1-\cos 2x)}\) for \(0<x<\pi/2\).
Answer: x
- The radicand becomes cos²x/sin²x.
- Cotangent is positive on the given interval, so the square root equals cot x.
- Since x is in the principal arccotangent range, the result is x.
Alternative 2 2 Marks
Evaluate \(\sin(\tan^{-1}(-\sqrt3)-\sec^{-1}2)\).
Answer: −√3/2
- The principal arctangent equals −π/3.
- The principal arcsecant equals π/3. Subtract to obtain −2π/3.
- Its sine is −√3/2.