CBSE Class 12 Mathematics 2026 Main Paper 65/1/3 · Q232 Marksprincipal_values
CBSE Class 12 Mathematics 2026 Main Paper 65/1/3 · Question 23 (Inverse Trigonometric Functions)
Simplify \(\sin^{-1}\sqrt{(1+\cos 2x)/2}\), for \(0<x<\pi/2\). OR Evaluate \(\cos(\sin^{-1}(-1)-\tan^{-1}(-\sqrt3))\).
Alternative 1 2 Marks
Simplify \(\sin^{-1}\sqrt{(1+\cos 2x)/2}\), for \(0<x<\pi/2\).
Answer: π/2−x
- Use 1+cos 2x=2 cos²x.
- The square root is cos x, which equals sin(π/2−x).
- The angle π/2−x is principal, so it is the result.
Alternative 2 2 Marks
Evaluate \(\cos(\sin^{-1}(-1)-\tan^{-1}(-\sqrt3))\).
Answer: √3/2
- The inverse sine gives −π/2 and the inverse tangent gives −π/3.
- Their difference is −π/6.
- The cosine is √3/2.