Question

sum the solutions of 2sin (x + 20) -1 = 0 equation over the range (0 °; 180 °)

Answer 1

The given equation is

$2sin(x+20)-1=0$

Adding 1 to both sides

$2sin(x+20)=1$

Dividing both sides by 2

$sin(x+20) = \frac{1}{2}$

Taking inverse sine

$x+20 = sin^{-1}( \frac{1}{2} )$

$x+20 = 30 , 150$

Subtracting 20 from both solutions

$x=10^\circ , 120^\circ$

And there sum is

$sum = 10 ^\circ + 120^\circ = 130^\circ$