What is ((sin(x))/2+(cos(x))/2)^2 ?

The solution to ((sin(x))/2+(cos(x))/2)^2 is (sin(2x)+1)/4

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simplify ((sin(x))/2+(cos(x))/2)^2

simplify

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

\frac{sin ( 2 x ) + 1}{4}

Solution steps

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

Join

\frac{sin ( x )}{2} + \frac{cos ( x )}{2} : \frac{sin ( x ) + cos ( x )}{2}

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

2^{2} = 4

= \frac{( sin ( x ) + cos ( x ) ) ^{2}}{4}

Simplify

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

= \frac{sin ( 2 x ) + 1}{4}

64 m^{6} - 729 n^{6}

a^{4} + 16 a^{2} + 64

(3 a + 5 b)^{3}

x^{2} - ln (x^{2}) + k

(a + b)^{11}

What is ((sin(x))/2+(cos(x))/2)^2 ?
The solution to ((sin(x))/2+(cos(x))/2)^2 is (sin(2x)+1)/4