Question

Use basic identities to simplify the expression.
sin θ cos θ sec θ csc θ

Answer 1

The simplified solution is 1

Explanation:

We need to solve the given trigonometric identity ;

`\sin\theta \cos \theta \sec \theta cosec \theta`

Since,
`cosec \theta =(1)/(\sin \theta)` and
`sec \theta =(1)/(\cos \theta)`

`\sin \theta \cos \theta (1)/(\cos \theta) (1)/(\sin \theta)`

`\sin \theta (1)/(\sin \theta) \cos \theta (1)/(\cos \theta)`

`1* 1`

`1`

Therefore, the simplified solution is 1

Answer 2

sin x cos x sec x csc x

= (sin x csc x) (cos x sec x)

= 1 x 1

= 1

Hope this helps