Is cos(3x)=(sqrt(2))/2 ?

The answer to whether cos(3x)=(sqrt(2))/2 is False

Popular >

prove cos(3x)=(sqrt(2))/2

prove

cos (3 x) = \frac{2}{2}

False

Solution steps

cos (3 x) = \frac{2}{2}

Show that the two sides are not equal

For

cos (3 x) = \frac{2}{2}

plug in

x = 0

cos (3 \cdot 0) = 1

cos (3 \cdot 0)

Simplify

= 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

cos (x) (sec (x) tan (x)) = tan (x)

cos (x) = \frac{sin ( x )}{tan ( x )}

cot^{2} (x) \cdot sec^{2} (x) = csc^{2} (x)

cot (\frac{1}{2} x) = \frac{sin ( x )}{1 - cos ( x )}

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