Answer to Question #5385 in Trigonometry for Akhtar Rasool khan
sir please help me in solving the question
If sintheta +costheta=1 then solve for theta.
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.