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Popular >

simplify (1-cos(2x))^2

Solution

simplify

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

Solution

4 sin^{4} (x)

Solution steps

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

Simplify

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

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

Apply exponent rule:

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

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

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

2^{2} = 4

= 4 (sin^{2} (x))^{2}

Apply exponent rule:

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

assuming

a \geq 0

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

= 4 sin^{2 \cdot 2} (x)

Multiply the numbers:

2 \cdot 2 = 4

= 4 sin^{4} (x)

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Frequently Asked Questions (FAQ)

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