What is the value of cos(15)cos(30)-sin(15)sin(30) ?

The value of cos(15)cos(30)-sin(15)sin(30) is (sqrt(2))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(15)cos(30)-sin(15)sin(30)

cos (1 5^{\circ}) cos (3 0^{\circ}) - sin (1 5^{\circ}) sin (3 0^{\circ})

\frac{2}{2}

Solution steps

cos (1 5^{\circ}) cos (3 0^{\circ}) - sin (1 5^{\circ}) sin (3 0^{\circ})

Rewrite using trig identities:

cos (1 5^{\circ}) = \frac{6 + 2}{4}

Use the following trivial identity:

cos (3 0^{\circ}) = \frac{3}{2}

Rewrite using trig identities:

sin (1 5^{\circ}) = \frac{6 - 2}{4}

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

= \frac{6 + 2}{4} \cdot \frac{3}{2} - \frac{6 - 2}{4} \cdot \frac{1}{2}

Simplify

\frac{6 + 2}{4} \cdot \frac{3}{2} - \frac{6 - 2}{4} \cdot \frac{1}{2} : \frac{2}{2}

= \frac{2}{2}

cos (4 \cdot π)

csc (12 7^{\circ})

csc (- 66 0^{\circ})

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

tan^{2} (2)

What is the value of cos(15)cos(30)-sin(15)sin(30) ?
The value of cos(15)cos(30)-sin(15)sin(30) is (sqrt(2))/2