Solve: 1/sqrt(2)(sin Theta + cos Theta) = cos Theta for Theta in (0, pi/2) ?

1 Answer
Jan 14, 2016

Theta = pi/8 rad = 22.5^o for Theta in (0, pi/2)

Explanation:

sin(A+B)=sin A cos B + cos A sin B

Thus: sin(Theta + pi/4) = sin Theta . cos (pi/4) + cos Theta . sin (pi/4)

= sin Theta . 1/sqrt(2) + cos Theta . 1/sqrt(2)

Therefore from the equation in the question:

sin Theta . 1/sqrt(2) + cos Theta . 1/sqrt(2) = cos Theta

Divide through by cos Theta

tan Theta . 1/sqrt(2) + 1/sqrt(2) = 1

tan Theta + 1 = sqrt(2)

tan Theta = sqrt(2) - 1

Theta = arctan(sqrt(2) - 1)

Theta = pi/8 rad = 22.5^o for Theta in (0, pi/2)