Question

Sec^2 theta/tan theta = sec theta x csc theta

Answer 1

see explanation

Explanation:

Using the trigonometric identities

• tan x =
`(sinx)/(cosx)`

• sec x =
`(1)/(cosx)`, csc x =
`(1)/(sinx)`

Consider the left side with x = Θ

`(sec^2x)/(tanx)`

=
`(1/cos^2x)/((sinx)/(cosx) )`

=
`(1)/(cos^2x)` ×
`(cosx)/(sinx)`

=
`(1)/(cosxsinx)`

=
`(1)/(cosx)` ×
`(1)/(sinx)`

= secxcscx = right side ⇒ verified