What is expand 1+sin(x)(1-sin(x)) ?

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

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expand 1+sin(x)(1-sin(x))

expand

1 + sin (x) (1 - sin (x))

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

Solution steps

1 + sin (x) (1 - sin (x))

Expand

sin (x) (1 - sin (x)) : sin (x) - sin^{2} (x)

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

Use the Pythagorean identity:

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

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

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

\frac{( x ^{4} + 3 x + 1 ) ^{5}}{( x ^{4} - 3 x ^{2} + 1 ) ^{4}}

(1 + sin (x)) (1 + cos (x))

\frac{( x ^{4} + 1 ) ^{2}}{x ^{8} + 1}

(x^{3} - x + 30)^{6}

(3 + 2)^{5}

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