What is (sin(a)+cos(a))^2-(sin(a)-cos(a))^2 ?

The solution to (sin(a)+cos(a))^2-(sin(a)-cos(a))^2 is 2sin(2a)

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simplify (sin(a)+cos(a))^2-(sin(a)-cos(a))^2

simplify

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

2 sin (2 a)

Solution steps

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

Simplify

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

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

Expand

- (sin (a) - cos (a))^{2} : sin (2 a) - 1

= sin (2 a) + 1 + sin (2 a) - 1

Group like terms

= sin (2 a) + sin (2 a) + 1 - 1

Add similar elements:

sin (2 a) + sin (2 a) = 2 sin (2 a)

= 2 sin (2 a) + 1 - 1

Subtract the numbers:

1 - 1 = 0

= 2 sin (2 a)

\frac{9 \cdot ( 3 + y )}{3}

- 8 x - 3

(5 x^{4} y^{3} z)^{2} (x^{4} y)^{3}

\frac{2}{5} (\frac{1}{3} x - \frac{15}{8}) - \frac{1}{3} (\frac{1}{2} - \frac{2}{3} x)

4 x^{2} + 5 2 x - 3

What is (sin(a)+cos(a))^2-(sin(a)-cos(a))^2 ?
The solution to (sin(a)+cos(a))^2-(sin(a)-cos(a))^2 is 2sin(2a)