The answer to whether 3-6sin^2(x)=0 is False

prove 3-6sin^2(x)=0

Solution

prove

3 - 6 sin^{2} (x) = 0

False

Solution steps

3 - 6 sin^{2} (x) = 0

Show that the two sides are not equal

For

3 - 6 sin^{2} (x) = 0

plug in

x = 0

3 - 6 sin^{2} (0) = 3

3 - 6 sin^{2} (0)

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

= 3 - 6 \cdot 0^{2}

Simplify

= 3

The two sides are not equal

\Rightarrow False

p ro v e cos^{4} (θ) = \frac{1}{4} + \frac{cos ( 2 θ )}{2} + \frac{cos ^{2} ( 2 θ )}{4}

p ro v e sin (x) (tan^{2} (x) + 1) = tan (x) sec (x)

p ro v e csc (u) = 2

p ro v e csc (x) - cos^{2} (x) - csc (x) = sin (x)

p ro v e 1 - \frac{cos ^{2} ( x )}{1 + sin ^{2} ( x )} = sin (s)