Solving trigonometric equations! Help!

Question

anonymous · Answer

How did 3(1-cos^2x)+cos^2x = 2

Became: 3 - 2cos^2x=2 ?! Could you guys help me with this one!

anonymous · Answer

Why didnt we multiple 3 by (1 - cos^2x) as a whole? Thanks!

campbell_st · Answer

you need to solve for x

so start with $$1 - \cos^2(x) = \sin^2(x)  $$

and substituting will give 

$$3\sin^2(x) + \cos^2(x) = 2$$

or 

$$2 \sin^2(x) + \sin^2(x) + \cos^2(x) = 1$$

and $$\sin^2(x) + \cos^2(x) = 1$$

so you have 

$$2 \sin^2(x) + 1 = 2$$

or 

$$2\sin^2(x) = 1$$

you should be able to solve for x now

in my solution I've tried to show every step so you can follow it... there are quicker solutions...