prove cos(θ)= 4/5

Solution

prove

cos (θ) = \frac{4}{5}

False

Solution steps

cos (θ) = \frac{4}{5}

Show that the two sides are not equal

For

cos (θ) = \frac{4}{5}

plug in

θ = 0

cos (0) = 1

cos (0)

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

= 1

The two sides are not equal

\Rightarrow False

\frac{2 sin ( 2 θ ) cos ( θ )}{2 sin ( 2 θ )} = cos (θ)

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

sin (x) (sec (x) tan (x)) = tan^{2} (x)

sin ((3 θ + 72)^{\circ}) = cos (4 8^{\circ})

tan (θ) + cot (θ) = \frac{1}{sin ( θ ) cos ( θ )}