Question

Find the value of cos24°+cos5°+cos175°+cos204°+cos300°

Answer 1

Hey there !!!!!!

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

=cos24°+cos5°+cos175°+cos204°+cos300°


cos∅ is positive when ∅ lies in first and fourth quadrants.

cos∅ is negative when ∅ lies in second and third quadrants.

cos175= cos(180-5)

But cos∅=cos(180-θ)= -cosθ

So, cos175= -cos5

cos204=cos(180+24)

But  cos∅=cos(180+θ)= -cosθ

cos204=-cos24

cos300= cos(270+30)

But  cos∅=cos(270+θ)= sinθ

So, cos300=sin30

Now,

=cos24°+cos5°+cos175°+cos204°+cos300°

=cos24°+cos5°-cos5°-cos24°+sin30°

=sin30°= 1/2 =0.5

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Hope this helped you....................