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

1 Answer
May 15, 2018

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