prove sin(u)= 1/4

Solution

prove

sin (u) = \frac{1}{4}

False

Solution steps

sin (u) = \frac{1}{4}

Show that the two sides are not equal

For

sin (u) = \frac{1}{4}

plug in

u = 0

sin (0) = 0

sin (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

= 0

The two sides are not equal

\Rightarrow False

tan (θ) + cot (θ) - sec (θ) csc (θ) = 0

\frac{sin ( 6 x ) - sin ( 2 x )}{cos ( 6 x ) - cos ( 2 x )} = - cot (4 x)

1 + cot^{2} (a) = csc^{2} (a)

\frac{2 cos ( x )}{cos ( x ) + cos ^{2} ( x )} = 2

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