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

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

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

prove

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

True

Solution steps

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

Manipulating left 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

sin^{2} (2 x) = \frac{1}{2} (1 - cos (4 x))

sec (t) - \frac{cos ( t )}{1 + sin ( t )} = tan (t)

sec (x) - cos (x) = sin (x) \cdot tan (x)

tan (\frac{x}{2}) = \frac{tan ( x )}{sec ( x ) + 1}

- cos (2 θ) = \frac{tan ^{2} ( θ ) - 1}{1 + tan ^{2} ( θ )}

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