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

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

Popular >

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

prove

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

True

Solution steps

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

Manipulating right side

1 + sin (2 x)

Use the Pythagorean identity:

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

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

Use the Double Angle identity:

sin (2 x) = 2 sin (x) cos (x)

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

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

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

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

We showed that the two sides could take the same form

\Rightarrow True

csc (θ) - csc (θ) cos^{2} (θ) = sin (θ)

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

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

cot (2 β) = \frac{cot ^{2} ( β ) - 1}{2 cot ( β )}

csc^{2} (y) tan^{2} (y) - 1 = tan^{2} (y)

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