Question

Simplify: (sin Θ − cos Θ)^2 + (sin Θ + cos Θ)^2

Answer 1

Hope this could help you

Answer 2

Answer:  The required simplified value of the given expression is 2.

Step-by-step explanation:  We are given to simplify the following trigonometric expression :

$T_E=(\sin\theta-\cos\theta)^2+(\sin\theta+\cos\theta)^2~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be using the following formulas :

$(i)~(a-b)^2=a^2-2ab+b^2,\\\\(ii)~(a+b)^2=a^2+2ab+b^2,\\\\(iii)~\sin^2\theta+\cos^2\theta=1.$

From (i), we have

$T_E\\\\=(\sin\theta-\cos\theta)^2+(\sin\theta+\cos\theta)^2\\\\=\sin^2\theta-2\sin\theta\cos\theta+\cos^2\theta+\sin^2\theta+2\sin\theta\cos\theta+\cos^2\theta\\\\=2(\sin^2\theta+\cos^2\theta)\\\\=2\times1\\\\=2.$

Thus, the required simplified value of the given expression is 2.