Which of the following is NOT equivalent to 1?

Question

A. (sin x + cos x)^2 - sin (2x)

B. 2 (sin x)^2 + cos (2x)

C. cos (2x) - 2 (cos x)^2

D. 8 (sin x cos x)^2 + cos (4x)

Answer 1

only C is not equal to 1

C = -1

A = 1

(sinx + cox)^2 - sin(2x)

'= sin^2(x) + 2sinxcosx + cos^2(x) - 2sinxcos

= sin^2(x) + cos^2(x) = 1

B = 1

2sin^2(x) + cos(2x)

= 2sin^2(x) + cos^2(x) - sin^2(x)

= sin^2(x) + cos^2(x) = 1

C does not equal 1, it equals -1

cos(2x) - 2cos^2(x)

= cos^2(x) - sin^2(x) - 2cos^2(x)

= -sin^2(x) - cos^2(x) = -1

D equals 1

8(sinxcosx)^2 + cos(4x)

=2(2sinxcosx)^2 + cos^2(2x) - sin^2(2x)

= 2(sin(2x)^2) - sin^2(2x) + cos^2(2x)

= sin^2(2x) + cos^2(2x) = 1