Question

If f(x) = `|(cos^2x, cosx.sinx, -sinx),(cosx sinx, sin^2x, cosx),(sinx, -cosx, 0)|`, then for all x

Options

• f(x) = 0

• f(x) = 1

• f(x) = 2

• None of these

Answer 1

f(x) = 1

Explanation:

We have `|(cos^2x, cosx.sinx, -sinx),(cosx sinx, sin^2x, cos x),(sin x, -cosx, 0)|`

= `|(1, 0, -sin x),(0, 1, cos x),(sin x, - cos x, 0)|`  ......[Applying C₁ → C₁ – sin x . C₃ and C₂ → C₂ + cos x . C₃]

= `|(1, 0, - sin x),(0, 1, cos x),(0, - cos x, sin^2x)|` .....[Applying R₃ → R₃ – sin x . R₁]

= sin²x + cos²x = 1 for all x.  .......[Expanding along C₁]