prove sec(4x)=2

Solution

prove

sec (4 x) = 2

False

Solution steps

sec (4 x) = 2

Show that the two sides are not equal

For

sec (4 x) = 2

plug in

x = 0

sec (4 \cdot 0) = 1

sec (4 \cdot 0)

Simplify

= sec (0)

Use the following trivial identity:

sec (0) = 1

sec (0)

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 1

= 1

The two sides are not equal

\Rightarrow False

\frac{1}{cos ^{2} ( A )} + \frac{1}{cot ^{2} ( A )} = 1

csc (θ) - sin (θ) = cot (θ) csc (θ)

cos (8 θ) = cos^{2} (4 θ) - sin^{2} (4 θ)

2 sec (2 α) cos (2 α) = 2

\frac{1}{sec ( x )} + 1 = \frac{sec ( x ) + 1}{sec ( x )}