Prove Sin theta = tan theta / sqrt 1+tan^2 theta. Hint: Solve for sin^2 in number 14.

Here is number 14:

sin^2 theta / 1-sin^2 theta = tan^2 theta

If you know all the trig identities you don't need to solve 14. The trig identities you need to know are tan=sin/cos. Sec=1/cos. And 1+tan^2 = sec^2

(I'll be replacing theta with x to make it easier to type)

Problem: sinx=tanx/sqrt 1+tanx^2.

Since 1+tanx^2=secx ^2

Sinx=tanx/sqrt secx^2

Sinx=tanx/secx

Now tanx = sinx/cosx and secx=1/cosx

(Sinx/cosx) / (1/cosx). The cosx cancel out leaving sin

So sinx=sinx