prove sin(A)= 3/5

Solution

prove

sin (A) = \frac{3}{5}

False

Solution steps

sin (A) = \frac{3}{5}

Show that the two sides are not equal

For

sin (A) = \frac{3}{5}

plug in

A = 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

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

cos (2 x) = cos (- 2 x)

tan (x) \cdot csc (x) = sec (x)

tan (θ) sin (θ) = 2 sin^{2} (θ)

- 2 cos^{2} (θ) = sin^{4} (θ) - cos^{4} (θ) - 1