Answer to Question #5385 in Trigonometry for Akhtar Rasool khan

Question

sir please help me in solving the question
If sintheta +costheta=1 then solve for theta.

Answer 1

Square both sides:
(sin x )^2 +(cos x)^2 + 2 sin x cos x = 1
as 2sinx cos x = sin 2x, then sin2x = 0.
As in trigonometric equations
sin x = 0, then x = n*pi
where n is an integer, thus
2x = n*pi and x = n*pi/2. As we used squaring not all obtained roots fit our initial problem
By inspection method put 1,2,3,4 etc as the value of n and see if the conditions are satisfied.
The values satisfying the conditions are x = 2(pi)k and x = pi/2+2(pi)k where k - integer, 2pi-period of sine and cosine functions.