Question

Simplify the function: sin⁻¹ (2 cos² θ - 1) + cos⁻¹ ( 1 - 2 sin² θ).

Answer 1

Answer:

$\frac{\pi}{2}$

Step-by-step explanation:

Formula used:

$cos2A=1-2{sin}^2A\\cos2A=2{cos}^2A-1$

${sin}^-1[2{cos}^2\theta-1]+{cos}^-1[1-2{sin}^2\theta]\\\\={sin}^-1[cos2\theta]+{cos^-1[cos2\theta]$

$={sin}^-1[sin(\frac{\pi}{2}-2\theta)]+{cos^-1[cos2\theta]$

$= \frac{\pi}{2}-2\theta+2\theta\\\\=\frac{\pi}{2}$