Question

Can someone help me prove the identity 2 - csc(β)sin(β) = sin^2(β) + cos^2(β)?

A) Yes, the identity can be proven using trigonometric properties.
B) No, this identity is not valid.
C) The identity can be proven, but additional information is needed.
D) It's not possible to prove this identity.
E) None of the above.

Answer 1

To prove the identity 2 - csc(β)sin(β) = sin^2(β) + cos^2(β), we can use trigonometric properties.

Step-by-step explanation:

To prove the identity 2 - csc(β)sin(β) = sin^2(β) + cos^2(β), we can use trigonometric properties.

First, let's express everything in terms of sine and cosine:

2 - (1/sin(β))sin(β) = sin^2(β) + cos^2(β)

Next, simplify the left side:

2 - 1 = sin^2(β) + cos^2(β)

Finally, apply the Pythagorean identity sin^2(β) + cos^2(β) = 1 to get:

1 = 1

Therefore, the identity is proven.