Is sin^2(2x)=4sin^2(x)*cos^2(x) ?

The answer to whether sin^2(2x)=4sin^2(x)*cos^2(x) is True

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prove sin^2(2x)=4sin^2(x)*cos^2(x)

prove

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

True

Solution steps

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

Manipulating left side

sin^{2} (2 x)

Rewrite using trig identities

sin^{2} (2 x)

Use the Double Angle identity:

sin (2 x) = 2 sin (x) cos (x)

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

Simplify

(2 sin (x) cos (x))^{2} : 4 sin^{2} (x) cos^{2} (x)

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

Apply exponent rule:

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

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

2^{2} = 4

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{sec ( x ) csc ( x )}{2} = csc (2 x)

- sec^{2} (x) = - tan^{2} (x) - 1

tan (4 x) \cdot cos (4 x) = sin (4 x)

\frac{sec ( x )}{cos ( x )} = \frac{1}{cos ^{2} ( x )}

tan (θ) = csc (θ) sec (θ) - cot (θ)

Is sin^2(2x)=4sin^2(x)*cos^2(x) ?
The answer to whether sin^2(2x)=4sin^2(x)*cos^2(x) is True