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

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

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

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

z = 0

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

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

Simplify:

2 \cdot 0 = 0

2 \cdot 0

Apply rule

0 \cdot a = 0

= 0

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

= - \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

cot (- x) sin (- x) = cos (x)

tan (\frac{7 u}{2}) = csc (7 u) - cot (7 u)

(sin (x) + cos (x)) 2 = 2 cos (x) sin (x) + 1

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

(sin (x) + 1)^{2} + cos^{2} (x) = 2

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