Question

Which double-angle or half-angle identity would you use to verify the following:

csc x sec x = 2 csc 2x
a.
cos 2x = 1-2 sin²x
b. sin 2x=2 sinx cosx
C.
d.
2tanx
1-tan²x
cos 2x = 2 cos²x-1
tan 2x
Please select the best answer from the choices provided
=

Answer 1

The double-angle identity that can be used to verify the equation csc x sec x = 2 csc 2x is option b. sin 2x=2 sinx cosx.

Step-by-step explanation:

The double-angle identity that can be used to verify the equation csc x sec x = 2 csc 2x is option b. sin 2x=2 sinx cosx.

To verify this, we can substitute csc x = 1/sin x and sec x = 1/cos x in the equation. We get:

(1/sin x) * (1/cos x) = 2 * (1/sin 2x)

Simplifying both sides gives us (1/sin x * cos x) = 2/sin 2x, which is the same as sin 2x = 2sin x * cos x.