What is the value of (cos(120)+sec(180))/(csc(270)+sin(330)) ?

The value of (cos(120)+sec(180))/(csc(270)+sin(330)) is 1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(cos(120)+sec(180))/(csc(270)+sin(330))

\frac{cos ( 12 0 ^{\circ} ) + sec ( 18 0 ^{\circ} )}{csc ( 27 0 ^{\circ} ) + sin ( 33 0 ^{\circ} )}

1

Solution steps

\frac{cos ( 12 0 ^{\circ} ) + sec ( 18 0 ^{\circ} )}{csc ( 27 0 ^{\circ} ) + sin ( 33 0 ^{\circ} )}

Use the following trivial identity:

cos (12 0^{\circ}) = - \frac{1}{2}

Use the following trivial identity:

sec (18 0^{\circ}) = (- 1)

Rewrite using trig identities:

csc (27 0^{\circ}) = - 1

Rewrite using trig identities:

sin (33 0^{\circ}) = - \frac{1}{2}

= \frac{- \frac{1}{2} - 1}{- 1 - \frac{1}{2}}

Simplify

\frac{- \frac{1}{2} - 1}{- 1 - \frac{1}{2}} : 1

= 1

10 \cdot cos (4 0^{\circ})

cos (78 0^{\circ})

50 cos (4 0^{\circ})

10 sin (3 5^{\circ})

5 cos^{2} (π)

What is the value of (cos(120)+sec(180))/(csc(270)+sin(330)) ?
The value of (cos(120)+sec(180))/(csc(270)+sin(330)) is 1