Question

cosx+√3sinx=2
what is the value of x?​

Answer 1

Answer:

x = 60°

Step-by-step explanation:

$cos x + \sqrt{3} sin x +=2$

$\\\sqrt{3} sinx =2 - cosx$

square both sides

$\\3sin^2 x = 4 -4cosx +cos^2 x$

$\\sin^2 x = 1- cos^2 x \\3(1-cos^2 x) = 4 -4 cosx + cos^2 x\\3 -3 cos^2x = 4 - 4 cosx +cos^2 x \\0 = 1 - 4 cos x + 4cos^2 x \\\\0 = (1- 2cos x)^2\\0 = 1- 2cosx \\2cosx = 1 \\cosx =1/2$

x =60°