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

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

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

prove

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

True

Solution steps

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

Manipulating right 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

tan (- \frac{π}{4}) = - 1

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

csc (x) sec (x) = 2 csc (2 x)

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

2 sec^{2} (x) - 2 cot^{2} (\frac{π}{2} - x) = 2

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