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

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

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

prove

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

True

Solution steps

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

Manipulating left side

(cos (x) + sin (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)

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

We showed that the two sides could take the same form

\Rightarrow True

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

1 - cos^{2} (x) + 3 = 2 sin (x) + 3

\frac{- 1 + sec ^{2} ( a )}{- tan ( a )} = - tan (a)

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

\frac{tan ( x )}{csc ( x )} = \frac{1}{cos ( x )} - \frac{1}{sec ( x )}

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