Question

Prove
`\:(cos\theta )/(sec\theta )+(sin\theta )/(csc\theta )=1`

Answer 1

see explanation

Explanation:

Using the identities

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

sin²x + cos²x = 1

Consider the left side

`(cos0)/(sec0)` +
`(sin0)/(csc0)`

=
`(cos0)/((1)/(cos0) )` +
`(sin0)/((1)/(sin0) )`

= cos²Θ + sin²Θ

= 1 = right side , thus proven