prove cos(θ)=3

Solution

prove

cos (θ) = 3

False

Solution steps

cos (θ) = 3

Show that the two sides are not equal

For

cos (θ) = 3

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

1.5 sin (2 a) cos (2 a) = sin (3 a)

\frac{1}{1 - cot ( x )} = 1 - tan (x)

\frac{5 sin ( 2 x )}{2} = \frac{5}{2} (2 sin (x) cos (x))

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

1 + (tan (a))^{2} = 1 + tan^{2} (a)