Question

cos 24° + cos 5° + cos 175° + cos 204° + cos 300°

Answer 1

Cos24°+Cos5°+Cos175°+Cos204°+Cos300°=
cos(90-66°)+cos(180-175°)+cos175°+cos(270-66°)+cos(360-66°)=
sin66°-cos175°+cos175°-sin66°+cos60°=
cos60°=1/2

Answer 2

Answer:

The value of cos 24° + cos 5° + cos 175° + cos 204° + cos 300° is 0.5.

Step-by-step explanation:

Consider the provide expression.

cos24° + cos5° + cos175° + cos204° + cos300°

The value of cos∅ is positive in first and fourth quadrants and the value of cos∅ is negative in second and third quadrants.

The Trigonometrical Ratios rule:

cos(180°-θ)= -cosθ

cos(180°+θ)= -cosθ

cos(270°+θ)= sinθ

Therefore,

cos175°= cos(180°-5°)  

So, cos175°= -cos5°     [∴cos(180°-θ)= -cosθ]

Now consider cos204°

cos204° = cos(180°+24°)

cos204° = -cos24°       [∴cos(180°+θ)= -cosθ]

Now consider cos300°

cos300° = cos(270°+30°)

cos300° = sin30°         [∴cos(270°+θ)= sinθ]

Substitute the respective values in the provided equation.

cos24°+cos5°+cos175°+cos204°+cos300°

cos24°+cos5°-cos5°-cos24°+sin30°

sin30°= 1/2 = 0.5

Hence, the value of cos 24° + cos 5° + cos 175° + cos 204° + cos 300° is 0.5.