Is (-3sin^2(2x))/2 =(3cos(4x))/4 ?

The answer to whether (-3sin^2(2x))/2 =(3cos(4x))/4 is False

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prove (-3sin^2(2x))/2 =(3cos(4x))/4

prove

\frac{- 3 sin ^{2} ( 2 x )}{2} = \frac{3 cos ( 4 x )}{4}

False

Solution steps

\frac{- 3 sin ^{2} ( 2 x )}{2} = \frac{3 cos ( 4 x )}{4}

Show that the two sides are not equal

For

\frac{- 3 sin ^{2} ( 2 x )}{2} = \frac{3 cos ( 4 x )}{4}

plug in

x = 0

\frac{- 3 sin ^{2} ( 2 \cdot 0 )}{2} = 0

\frac{- 3 sin ^{2} ( 2 \cdot 0 )}{2}

Simplify

= - \frac{3 sin ^{2} ( 0 )}{2}

Use the following trivial identity:

sin (0) = 0

sin (0)

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

= - \frac{3 \cdot 0 ^{2}}{2}

Simplify

= 0

\frac{3 cos ( 4 \cdot 0 )}{4} = \frac{3}{4} (Decimal : 0.75)

\frac{3 cos ( 4 \cdot 0 )}{4}

Simplify

= \frac{3 cos ( 0 )}{4}

Use the following trivial identity:

cos (0) = 1

cos (0)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 1

= \frac{3 \cdot 1}{4}

Simplify

= \frac{3}{4}

The two sides are not equal

\Rightarrow False

p ro v e 8 sin^{4} (θ) = cos (4 θ) + 4 cos (2 θ) - 3

p ro v e sec^{2} (a) csc^{2} (a) = sec^{2} (a) + csc^{2} (a)

p ro v e cot (x) - tan (x) = 2 tan (2 x)

p ro v e 1 + cot (x) = \frac{cos ( x ) + sin ( x )}{sin ( x )}

p ro v e cos (3 b) = cos (b) (cos^{2} (b) - 3 sin^{2} (b))

Is (-3sin^2(2x))/2 =(3cos(4x))/4 ?
The answer to whether (-3sin^2(2x))/2 =(3cos(4x))/4 is False