How do you find the exact value of cos 70 cos 20 - sin 70 sin 20?

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How do you find the exact value of cos 70 cos 20 - sin 70 sin 20?

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Answer 1 · 2015-10-19T15:11:13

$cos (70^{\circ}) \cdot cos (20^{\circ}) - sin (70^{\circ}) \cdot sin (20^{\circ}) = 0$ $cos(70^@)*cos(20^@)-sin(70^@)*sin(20^@) = 0$

Explanation:

The Cosine Sum of Angles Formula tells us
$cos (a + b) = cos (a) \cdot cos (b) - sin (a) \cdot sin (b)$ $cos(a+b) = cos(a)*cos(b)-sin(a)*sin(b)$

Substituting $70^{\circ}$ $70^@$ for $a$ $a$
and $20^{\circ}$ $20^@$ for $b$ $b$

we have
$cos (90^{\circ}) = cos (70^{\circ}) \cdot cos (20^{\circ}) - sin (70^{\circ}) \cdot sin (20^{\circ})$ $cos(90^@)=cos(70^@)*cos(20^@)-sin(70^@)*sin(20^@)$
and we know
$cos (90^{\circ}) = 0$ $cos(90^@) = 0$

Answer 2 · 2015-10-19T15:12:33

Find (cos 70.cos 20 - sin 70.sin 20)

Ans: 0

Explanation:

Use the trig identity: cos (a + b) = cos a.cos b - sin a.sin b -->
(cos 70.cos 20 - sin 70.sin 20) = cos (70 + 20) = $cos (90^{\circ}) = 0$ $cos (90^@) = 0$

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How do you find the exact value of cos 70 cos 20 - sin 70 sin 20?

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