Question

What are some ways tanθ=sinθ/cos θ can be expressed?

Answer 1

See explanation

Explanation:

We can express

`\tan( \theta) = ( \sin \theta)/( \cos \theta )`

in so many ways using trigonometric identities.

Let us rewrite to obtain:

`\tan( \theta) = (1)/( \cos \theta ) * \sin \theta`

This implies that

`\tan( \theta) = \sec \theta \sin \theta`

When we multiply the right side by

`( \cos \theta)/( \cos \theta)`

we get:

`\tan( \theta) = ( \sin \theta \cos \theta )/( \cos ^(2) \theta )`

`\tan( \theta) = ( \sin 2\theta )/( 2 - 2\sin^(2) \theta )`

Etc