Question

Verify the identity below with work and/ or explanation. 2ab/sin^2θ = 2ab sec^2θ/sec^2θ-1

Answer 1

To verify the identity 2ab/sin²θ = 2ab sec²θ/sec²θ-1, we need to simplify both sides of the equation and check if they are equal.

Step-by-step explanation:

To verify the identity 2ab/sin²θ = 2ab sec²θ/sec²θ-1, we need to simplify both sides of the equation and check if they are equal.

Starting with the left side, we have: 2ab/sin²θ. We can rewrite this as 2ab(1/sin²θ).

Then, using the Pythagorean Identity sin²θ + cos²θ = 1, we substitute 1 - cos²θ for sin²θ.

Now, we can simplify the expression by canceling out common factors and using trigonometric identities. Eventually, we arrive at the right side of the equation, which is 2ab sec²θ/sec²θ-1.

Since both sides simplify to the same expression, we can conclude that the given identity is true.