Question

Cos 10° cos 50° cos 70° = underroot 3 / 8

Answer 1

Answer:

Step-by-step explanation:

(cos 10 cos 50) cos70

= $\frac{1}{2}$ ( 2cos10 cos50) cos70

= $\frac{1}{2}$ {(cos(50 + 10) + cos(50 - 10)} cos70

=  $\frac{1}{2}$ (cos60+ cos40) cos70.

we know cos 60 value is $\frac{1}{2}$. so this value will put in the next step

=  $\frac{1}{2}$ ($\frac{1}{2}$ + cos40) cos70

=  $\frac{1}{2}$ (cos70/2  + cos70 cos40)

=  $\frac{1}{2}$ (cos70 + cos70 cos40/2)    [ take LCM (2)]

=  $\frac{1}{4}$ (cos70 + 2 cos70 cos40)

=  $\frac{1}{4}$ (cos70 + cos110 + cos30)

=  $\frac{1}{4}$ (cos70 + cos(180 - 70) + cos30)

=  $\frac{1}{4}$ (cos70 - cos70 + cos30)   { -cos 70 is in 2nd quadrant.}

=  $\frac{1}{4}$ × $\frac{\sqrt{3} }{2}$

= $\frac{\sqrt{3} }{4 * 2}\\\\\frac{\sqrt{3}}{8}$

hence proved.