prove that: cos24°+cos55°+cos125°+cos204°+cos300°=1/2
Answers
The above mentioned question is from trignometry let solve it.
To prove that: cos24°+cos55°+cos125°+cos204°+cos300°=1/2
Here is the solution:
Cos (180°- 55°) = - cos 125°
cos (180°+ 24°) = -cos 24°
cos (360°-60°) = cos 60°
cos 24°- cos 125°+ cos 125°- cos 24°+ cos 60°
cos 60°= 1/2.
OR
cos 24°+ cos 55°+ cos 125°+ cos 204°+ cos 300°=1/2 hence proved.
show the explanation
cos(24)°
Since our angle is between 0 and 90 degrees, it is located in Quadrant I
In the first quadrant, the values for sin, cos and tan are positive.
24 is an acute angle since it is less than 90°
cos(24) = 0.91354545783728
cos(55)°
Since our angle is between 0 and 90 degrees, it is located in Quadrant I
In the first quadrant, the values for sin, cos and tan are positive.
55 is an acute angle since it is less than 90°
cos(55) = 0.57357643724956
cos(125)°
Since our angle is greater than 90 and less than or equal to 180 degrees, it is located in Quadrant II
In the second quadrant, the values for sin are positive only.
125 is an obtuse angle since it is greater than 90°
cos(125) = -0.57357643430897
Calculate cos(204)°
Since our angle is greater than 180 and less than or equal to 270 degrees, it is located in Quadrant III
In the third quadrant, the values for tan are positive only.
204 is an obtuse angle since it is greater than 90°
cos(204) = -0.91354545929738
cos(300)°
Since our angle is greater than 270 and less than or equal to 360 degrees, it is located in Quadrant IV
In the fourth quadrant, the values for cos are positive only.
300 is an obtuse angle since it is greater than 90°
cos(300) = 1/2
cos 24 + cos 55 ° + cos 125 ° + cos 204 ° + cos 300 ° = 0.5