Is (tan(θ+1))=sec(θ) ?

The answer to whether (tan(θ+1))=sec(θ) is False

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove (tan(θ+1))=sec(θ)

prove

(tan (θ + 1)) = sec (θ)

False

Solution steps

tan (θ + 1) = sec (θ)

Show that the two sides are not equal

For

tan (θ + 1) = sec (θ)

plug in

θ = 0

tan (0 + 1) = 1.55740 \dots

tan (0 + 1)

Refine to a decimal form

= 1.55740 \dots

sec (0) = 1

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{sin ( x ) csc ( x )}{cos ( x )} = sec (x)

tan (x) + sec (x) = 1

- sinh^{2} (x) + cosh^{2} (x) = 1

sin^{2} (x) + cos^{2} (x) - 1 = 0

sec (x) sin (\frac{π}{2} - x) = 1