Question

Rewrite 2cos75° sin75° using a double angle identity

Answer 1

2sinXcosX=sin(2x), so 2cos75sin75=sin(2*75)=sin150

Answer 2

2cos75° sin75° = sin150°.

Explanation:

Consider the provided information.

2cos75° sin75°

The double-Angle Identities of sin(2x) is:

2 sin(x) cos(x) = sin(2x)

Replace x with 75° in the above formula.

2 sin(75°) cos(75°) = sin(2(75°))

2 sin(75°) cos(75°) = sin(150°)

2 cos(75°) sin(75°) = sin(150°)

Now compare the above equation and the provided expression. By comparison it can be concluded that the provided expression is equivalent to sin 150°

Hence, 2cos75° sin75° = sin150°.