Is sec^4(x/3)=((sec^4(x)))/3 ?

The answer to whether sec^4(x/3)=((sec^4(x)))/3 is False

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove sec^4(x/3)=((sec^4(x)))/3

prove

sec^{4} (\frac{x}{3}) = \frac{( sec ^{4} ( x ) )}{3}

False

Solution steps

sec^{4} (\frac{x}{3}) = \frac{sec ^{4} ( x )}{3}

Show that the two sides are not equal

For

sec^{4} (\frac{x}{3}) = \frac{sec ^{4} ( x )}{3}

plug in

x = 0

sec^{4} (\frac{0}{3}) = 1

sec^{4} (\frac{0}{3})

Simplify

= sec^{4} (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^{4}

Simplify

= 1

\frac{sec ^{4} ( 0 )}{3} = \frac{1}{3} (Decimal : 0.33333 \dots)

\frac{sec ^{4} ( 0 )}{3}

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

= \frac{1 ^{4}}{3}

Simplify

= \frac{1}{3}

The two sides are not equal

\Rightarrow False

2 sin (z) cos (z) = sin (2 z)

sin (x) + \frac{cos ^{2} ( x )}{sin ( x )} = sec (x)

- tan (x) cos (x) = tan (x)

\frac{cos ( 3 θ )}{cos ( θ )} = 1 - 4 sin^{2} (θ)

9 sin (2 x) sin (x) = 9 cos (x)

Is sec^4(x/3)=((sec^4(x)))/3 ?
The answer to whether sec^4(x/3)=((sec^4(x)))/3 is False