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

Question

44423 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-19T15:11:13

#cos(70^@)*cos(20^@)-sin(70^@)*sin(20^@) = 0#

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

Substituting #70^@# for #a#
and #20^@# for #b#

we have
#cos(90^@)=cos(70^@)*cos(20^@)-sin(70^@)*sin(20^@)#
and we know
#cos(90^@) = 0#

Answer 2 · 2015-10-19T15:12:33

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

Ans: 0

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^@) = 0#