Trigenometric equation. (1 Viewer)

[deltaxray]

Can someone help me solve the following trig equations?


1. 5sin^2(x) -4sin(x) cos(x)+3cos^2(x) = 2

2. 3 tan(x)-2 cot(x)+3 sec(x) = 0

thanks.

 

[Lukybear]

1.5sin^2(x) -4sin(x) cos(x)+3cos^2(x) = 2

Divide everything by cos^2 or sin^2

5tan^2x-4tan^2x+3 = 2sec^2
5tan^2x-4tan^2x+3 = 2tan^2x+2
3tan^2x-4tanx+1=0
tanx = 1/3 or 1
x = 18degree 26 min, or 45 degree

 

[Lukybear]

2.3 tan(x)-2 cot(x)+3 sec(x) = 0

3(sinx/cosx) - 2(cosx/sinx) + 3/cosx = 0

3sin^2x - 2(cos^2x) + 3sinx = 0
simplify:
5sin^2x+3sinx-2 =0
etc...
solve

 

[Drongoski]

1 way:

 

[deltaxray]

Cheers guys

Thanks for the help