Is tan^2(0)=1-sec(0) ?

The answer to whether tan^2(0)=1-sec(0) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove tan^2(0)=1-sec(0)

prove

tan^{2} (0) = 1 - sec (0)

True

Solution steps

tan^{2} (0) = 1 - sec (0)

Manipulating left side

tan^{2} (0)

Simplify

tan^{2} (0) : 0

tan^{2} (0)

Simplify

tan (0) : 0

tan (0)

Use the following trivial identity:

tan (0) = 0

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 0

= 0^{2}

Apply rule

0^{a} = 0

= 0

= 0

Manipulating right side

1 - sec (0)

Simplify

1 - sec (0) : 0

1 - sec (0)

Use the following trivial identity:

sec (0) = 1

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

Simplify

= 0

= 0

We showed that the two sides could take the same form

\Rightarrow True

cos^{3} (A) = \frac{1}{4} (cos (3 A) + 3 cos (A))

\frac{sin ( 6 x ) - sin ( 2 x )}{cos ( 6 x ) - cos ( 2 x )} = - \frac{cos ( 4 x )}{sin ( 4 x )}

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

\frac{1}{sin ( x ) + 1} + \frac{1}{csc ( + 1 )} = 1

cos (x) = sin (x - π)