The answer to whether cos(θ)= 1/3 is False

prove cos(θ)= 1/3

Solution

prove

cos (θ) = \frac{1}{3}

False

Solution steps

cos (θ) = \frac{1}{3}

Show that the two sides are not equal

For

cos (θ) = \frac{1}{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

p ro v e sec (θ) - \frac{tan ( θ )}{csc ( θ )} = cos (θ)

p ro v e sec^{2} (x) = (1 + tan^{2} (x))

p ro v e cot^{2} (x) sec^{2} (x) = cot^{2} (x) + 1

p ro v e \frac{sin ( x )}{cos ( x ) + sin ( x )} = 1

p ro v e cos (x) = \frac{cot ( x )}{tan ( x )}