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

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

Popular >

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

prove

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

True

Solution steps

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

Manipulating right side

1 + sin (2 a)

Use the Pythagorean identity:

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

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

Use the Double Angle identity:

sin (2 a) = 2 sin (a) cos (a)

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

Apply Perfect Square Formula:

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

2 cos (x) (sin (3 x) - sin (x)) = sin (4 x)

\frac{1 - sin ( θ )}{sec ( θ )} = \frac{cos ^{3} ( θ )}{1 + sin ( θ )}

2 sin (θ) = 2 sin (θ) cos (θ)

5 sin^{2} (x) + 5 cos^{2} (x) = 5

cot (θ) = \frac{( 1 + cos ( 2 θ ) )}{sin ( 2 θ )}

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