Question

Use a double- angle identity to find the exact values for the following expressions: cos75 sin75 (Please provide work!) (T⌓T)

Answer 1

Answer:

2cos75° sin75° = sin150°.

Step-by-step 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°.

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