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Popular >

simplify (1+cos(2x))^3

Solution

simplify

(1 + cos (2 x))^{3}

Solution

8 cos^{6} (x)

Solution steps

(1 + cos (2 x))^{3}

Simplify

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

= (2 cos^{2} (x))^{3}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(2 cos^{2} (x))^{3} = 2^{3} (cos^{2} (x))^{3}

= 2^{3} (cos^{2} (x))^{3}

2^{3} = 8

= 8 (cos^{2} (x))^{3}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

(cos^{2} (x))^{3} = cos^{2 \cdot 3} (x)

= 8 cos^{2 \cdot 3} (x)

Multiply the numbers:

2 \cdot 3 = 6

= 8 cos^{6} (x)

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Frequently Asked Questions (FAQ)

What is (1+cos(2x))^3 ?
The solution to (1+cos(2x))^3 is 8cos^6(x)