| If then which of the following are correct?

1)

2) The value of the determinant of the matrix is 1.

3) The determinant of f(x) is an even function.

Select the correct answer using the code given below :

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

### Right Answer is: D

#### SOLUTION

f(θ) *f(Φ)=

*

f(θ) *f(Φ)=f(θ+Φ)

det[f(θ) *f(Φ)] = 1[cos^{2}(θ+Φ)+sin^{2}(θ+Φ)] =1

det(f(x)) = cos^{2}x-(-sin^{2}x) = cos^{2}x+sin^{2}x = 1

for x=-x, det f(-x) = cos^{2}(-x)-(-sin^{2}(-x))=cos^{2}x+sin^{2}x = 1

detf(-x) = detf(x)

f(x) is even function.