What is expand (1+sin(x))^2-cos^2(x) ?

The solution to expand (1+sin(x))^2-cos^2(x) is 1+2sin(x)+sin^2(x)-cos^2(x)

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expand (1+sin(x))^2-cos^2(x)

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

1^{2} + 2 \cdot 1 \cdot sin (x) + sin^{2} (x) : 1 + 2 sin (x) + sin^{2} (x)

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

(1 + \frac{x}{1 + \frac{x}{y}}) (x + y)

\frac{3 ( 9 - y )}{2}

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

\frac{- s ^{3} + 2 s ^{2} + 1}{s ^{2} ( s ^{2} + 1 )}

\frac{( x + 2 ) ( x ^{2} + 4 )}{x + 5}

What is expand (1+sin(x))^2-cos^2(x) ?
The solution to expand (1+sin(x))^2-cos^2(x) is 1+2sin(x)+sin^2(x)-cos^2(x)