Question

Solving trigonometric equations! Help!

Answer 1

How did 3(1-cos^2x)+cos^2x = 2

Became: 3 - 2cos^2x=2 ?! Could you guys help me with this one!

Answer 2

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

Answer 3

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...