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

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

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

prove

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

True

Solution steps

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

We showed that the two sides could take the same form

\Rightarrow True

cos^{2} (A) tan^{2} (A) = sin^{2} (A)

(1 - cos (x)) (1 + sec (x)) = sin (x)

csc (y) cos^{2} (y) + sin (y) = csc (y)

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

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

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