What is the value of 10cos(75)cos(15) ?

The value of 10cos(75)cos(15) is 5/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

10cos(75)cos(15)

10 cos (7 5^{\circ}) cos (1 5^{\circ})

\frac{5}{2}

Solution steps

10 cos (7 5^{\circ}) cos (1 5^{\circ})

Rewrite using trig identities:

5 (cos (6 0^{\circ}) + cos (9 0^{\circ}))

= 5 (cos (6 0^{\circ}) + cos (9 0^{\circ}))

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

cos (9 0^{\circ}) = 0

= 5 (\frac{1}{2} + 0)

Simplify

5 (\frac{1}{2} + 0) : \frac{5}{2}

= \frac{5}{2}

cos^{2} (\frac{5 π}{6}) - 2 sin (\frac{5 π}{6})

- sin (27 0^{\circ})

arcsin (sin (- \frac{7 π}{4}))

\frac{25}{sin ( 2 7 ^{\circ} )}

5 \cdot sin (3 0^{\circ})