prove 2sin^2(x)=1

Solution

prove

2 sin^{2} (x) = 1

False

Solution steps

2 sin^{2} (x) = 1

Show that the two sides are not equal

For

2 sin^{2} (x) = 1

plug in

x = 0

2 sin^{2} (0) = 0

2 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

= 2 \cdot 0^{2}

Simplify

= 0

The two sides are not equal

\Rightarrow False

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

sin^{2} (t) = \frac{1}{2} - \frac{1}{2} cos (2 t)

cos (3 x) = 4 (cos^{3} (x)) - 3 cos (x)

\frac{1 + csc ( x )}{sec ( x )} = cot (x) cos (x)

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