Question

can someone help me with this math problem please:) Verify the identity. Justify each step.

Answer 1

@Jhannybean

Answer 2

what is it?

Answer 3

\(\dfrac{\sec \theta}{\csc \theta - \cot \theta} - \dfrac{\sec \theta}{\csc \theta + \cot \theta} = 2 \csc \theta\)

\(\color{red}{\dfrac{\csc \theta + \cot \theta}{\csc \theta + \cot \theta}} \dfrac{\sec \theta}{\csc \theta - \cot \theta} - \color{green}{\dfrac{\csc \theta - \cot \theta}{\csc \theta - \cot \theta }} \dfrac{\sec \theta }{\csc \theta + \cot \theta} = 2 \csc \theta\)

\(\dfrac{\csc \theta \sec \theta + \cot \theta \sec \theta - \csc \theta \sec \theta + \cot \theta \sec \theta}{\csc^2 \theta - \cot^2 \theta} = 2 \csc \theta\)

\(\dfrac{\cancel{\csc \theta \sec \theta} - \cancel{\csc \theta \sec \theta} + 2\cot \theta \sec \theta}{\cancel{\csc^2 \theta - \cot^2 \theta}~~1} = 2 \csc \theta\)

\(2\cot \theta \sec \theta = 2 \csc \theta\)

\(2 \dfrac{\cancel{\cos \theta}}{\sin \theta} \dfrac{1}{\cancel{\cos \theta}} = 2 \csc \theta\)

\(\dfrac{2}{\sin \theta} = 2 \csc \theta\)

\(2 \csc \theta = 2 \csc \theta\)

Answer 4

thanks dudde:)

Answer 5

yw