Is 2sin(x)cos(x)+1=(sin(x)+cos(x))^2 ?

The answer to whether 2sin(x)cos(x)+1=(sin(x)+cos(x))^2 is True

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prove 2sin(x)cos(x)+1=(sin(x)+cos(x))^2

prove

2 sin (x) cos (x) + 1 = (sin (x) + cos (x))^{2}

True

Solution steps

2 sin (x) cos (x) + 1 = (sin (x) + cos (x))^{2}

Manipulating right side

(sin (x) + cos (x))^{2}

Expand

(cos (x) + sin (x))^{2} : cos^{2} (x) + 2 cos (x) sin (x) + sin^{2} (x)

= cos^{2} (x) + sin^{2} (x) + 2 cos (x) sin (x)

Rewrite using trig identities

= 1 + 2 cos (x) sin (x)

= 2 sin (x) cos (x) + 1

We showed that the two sides could take the same form

\Rightarrow True

1 - cos (θ) = sin (θ)

cos (2 π + x) = cos (x)

sin^{2} (x) sec^{2} (x) = \frac{1}{cot ^{2} ( x )}

sin (x) = cos (x)

sin (x) tan (x) cot^{2} (x) = cos (x)

Is 2sin(x)cos(x)+1=(sin(x)+cos(x))^2 ?
The answer to whether 2sin(x)cos(x)+1=(sin(x)+cos(x))^2 is True