Question

How do I show that both sides of these trigonometric identities are equal to each other?

1.) `sintheta = costhetatantheta`
2.) `sin^2theta-cos^2theta=1-2cos^2theta`

Answer 1

See explanation

Explanation:

...pretty straightforward, I think:
First one: `sin theta = cos theta tan theta`
...remember that `tan theta = (sin theta) /(cos theta)`
so:
`sin theta = cos theta * ((sin theta)/(cos theta))`

...and the `cos theta` terms on the right cancel out:

`sin theta = sin theta`

What you have to do for the second one is add `2cos^2 theta`
to both sides:

`sin^2 theta - cos^2 theta + 2 cos^2 theta = 1`
`sin^2 theta + cos^2 theta = 1`

...the above is a trig identity you should know by heart, so this shows that the original formula is a valid identity.

GOOD LUCK