# Answer to Question #5385 in Trigonometry for Akhtar Rasool khan

Question #5385

sir please help me in solving the question

If sintheta +costheta=1 then solve for theta.

If sintheta +costheta=1 then solve for theta.

Expert's answer

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.

(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.

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