Need help with finding the value using trigonometric identity

Question

Given: $\sin\alpha + \cos\alpha= \alpha$.

Determine the value of $\sin\alpha\times\cos \alpha$

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Answer 1

Given $\sin(\alpha)+\cos(\alpha)=a$, we find the value of $\sin(\alpha)\cos(\alpha)$. $$\sin(\alpha)+\cos(\alpha)=a\implies(\sin(\alpha)+\cos(\alpha))^2=a^2\implies\sin^2(\alpha)+2\cos(\alpha)\sin(\alpha)+\cos^2(\alpha)=a^2$$

by using $(x+y)^2=x^2+2xy+y^2$. Then recall $\cos^2(\alpha)+ \sin^2(\alpha)=1$. Can you go from here?

Answer 2

Square the equation and use the fact that. $$\sin^2x + \cos^2x = 1$$