Question

How do I solve this?

Answer 1

sec θ csc θ

Explanation:

identities: sin²θ + cos²θ = 1, sec θ = 1/cos θ, csc θ = 1/sin θ.

secθ csc θ = (1/cosθ) (1/sinθ) = 1/(cosθsinθ) = 1/(sinθcosθ)

tan θ + cot θ = sinθ/cosθ + 1/tan θ

= sin θ/cos θ + cosθ/sinθ

= (sin²θ + cos²θ) / (sinθ cosθ)

= 1/sinθcosθ

= 1/cosθsinθ

= sec θ csc θ