Question

prove the following trigonometric identities. Include reason with calculation:

secθ/tanθ=cscθ

Answer 1

sec θ / tan θ = csc θ

sec θ ÷ tan θ =

. 1. . . . . . sin θ
--------- ÷ ---------- =
cos θ . . . cos θ

. 1. . . . . . cos θ . . . . 1
--------- X ---------- = -------- = csc θ
cos θ . . . sin θ . . . sin θ

Answer 2

\[\frac{\sec(\theta)}{\tan(\theta)}=\frac{1}{\cos(\theta)} \times \frac{\cos(\theta)}{\sin(\theta)}=\frac{1}{\sin(\theta)}=\csc(\theta)\]