How Do You Solve a Trigonometric Equation Involving Both Sine and Cosine?

[Dell]

as part of a physics problem i get to one stage before the ansewr and then i get stuck here:

0.15348=0.1415cosβ -0.291sinβcosβ

how do i solve this equation with both sinβ and cosβ, i realize that i need to play with the identities but have had no luck,
please help

 

[rock.freak667]

Try squaring both sides and see if you can use sin²x+cos²x=1 in hopes to get one trig term.

 

[Dell]

copied it all wrong, sorry, obviously can't work,,,

meant to be

0.15348=0.1415cosβ -0.291sinβcosβ

if i square it i get

0.023556=0.02cos²β +0.085sin²βcos²β-0.08sinβcosβ

if i say cos²β=t

0.023556=0.02t + 0.085(1-t)*(t)-0.08*$$\sqrt{1-t}$$$$\sqrt{t}$$

0.023556=0.02t + 0.085t - 0.085t² -0.08$$\sqrt{t-t²}$$

0.023556=0.105t - 0.85t² - 0.08$$\sqrt{t-t²}$$

now how would i find t??

you sure there's no better way?