Determine all solutions of the equation in radians.
-$$( \sin x + \cos x ) ^ { 2 } = 1$$
A)Identity
B)Not an identity

Question

Quizplus · Accepted Answer

The equation is not an identity because it does not hold true for all values of $x$. An identity in trigonometry is an equation that is true for all values within the domain of the variables involved. The given equation, when expanded, becomes $\sin^2x + 2\sin x\cos x + \cos^2x = 1$. Using the Pythagorean identity $\sin^2x + \cos^2x = 1$, this simplifies to $2\sin x\cos x = 0$, which only holds true for specific values of $x$, not for all $x$.

Determine All Solutions of the Equation in Radians (sin⁡x+cos⁡x)2=1( \sin x + \cos x ) ^ { 2 } = 1(sinx+cosx)2=1

Determine All Solutions of the Equation in Radians $( \sin x + \cos x ) ^ { 2 } = 1$