Question

What are steps to:
Cos70°cos10°+cos20°cos80°
=

Answer 1

Solution :

____________________

i )cos20 = cos(90-70)

= sin70

ii ) cos80° = cos( 90 - 10 )

= sin10

________________________

cos70cos10+cos20cos80

= cos70cos10+sin70sin10

= cos( 70 - 10 )

= cos60

= 1/2

•••••

Answer 2

$\cos 70^\circ\cos 10^\circ+\cos 20^\circ\cos 80^\circ= \frac{1}{2}$

Step-by-step explanation:

Given : Expression $\cos 70^\circ\cos 10^\circ+\cos 20^\circ\cos 80^\circ$

To find : What are the steps to expression ?

Solution :

Using trigonometric properties, $\cos(90-\theta)=\sin \theta$

We can re-write terms as,

$\cos 20 = \cos(90-70)= \sin 70^\circ$

$\cos 80 = \cos(90-10)= \sin 10^\circ$

Substitute in the expression,

$=\cos 70^\circ\cos 10^\circ+\sin 70^\circ\sin 10^\circ$

Using trigonometric properties, $\cos(A-B)=\cos A\cos B+\sin A\sin B$

Here, A=70 and B=10

$= \cos(70 - 10)$

$= \cos 60^\circ$

$= \frac{1}{2}$

Therefore, $\cos 70^\circ\cos 10^\circ+\cos 20^\circ\cos 80^\circ= \frac{1}{2}$

#Learn more

Cos10°cos50°cos70°=√3/8

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