**2cos^2x=sinx+1; 0° less than equal to x less than equal to 360°**

**Answer:**

2cos^2x = sinx + 1

=>2(1-sin^2x) = sinx + 1 (Using the trigonometric identity, cos^2x + sin^2x = 1)

=>2 - 2sin^2x = sinx + 1

=>2sin^2x+sinx-1 = 0 ;

(This is a quadratic in sinx; factorising the equation or can solve for roots of the equation )

=>2sin^2x+2sinx-sinx-1 = 0

=>2sinx(sinx+1)-(sinx+1) = 0

=>(2sinx-1)(sinx+1)=0

=>sinx = 1/2 or sinx=-1;

sinx=1/2 => x=30 degrees or x=180-30 = 150 degrees ;

sinx=-1 => x= 180+90 = 270 degrees