the value of root 3cot60 - sec 60 is
Answers
Step-by-step explanation:
From the figure, draw the perpendicular line AD from A to the side BC
Now △ ABD≅ △ACD
So, BD=DC and also
∠ BAD=∠ CAD
It is observed that the triangle ABD is a right triangle, right angled at D with
∠ BAD=30° and∠ABD=60°
To find the trigonometric ratios, we need to know the lengths of the sides of the triangle. So, let us assume that AB=2a
BD = BC/2 = a
To find the value of cos 60°, it becomes
Cos θ = Adjacent Side / Hypotenuse Side
Cos 60°=Adjacent Side/Hypotenuse Side =BD/AB
Cos 60° = a/2a = ½
We know that secant function is the inverse function of the cosine function, it becomes
Sec 60° = 1/cos 60°
Sec 60° = 1/(½) = 2
Therefore, the value of sec 60 = 2
Sec 60°= 2
In the same way, we can derive other values of sec degrees like 0°, 30°, 45°, 90°, 180°, 270° and 360°. The values of secant function along with other trigonometric ratios are given in the below trigonometry table.
Trigonometry Ratio Table
Angles (In Degrees) 0 30 45 60 90 180 270 360
Angles (In Radians) 0 π/6 π/4 π/3 π/2 π 3π/2 2π
sin 0 1/2 1/√2 √3/2 1 0 −1 0
cos 1 √3/2 1/√2 1/2 0 −1 0 1
tan 0 1/√3 1 √3 Not Defined 0 Not Defined 0
cot Not Defined √3 1 1/√3 0 Not Defined 0 Not Defined
cosec Not Defined 2 √2 2/√3 1 Not Defined −1 Not Defined
sec 1 2/√3 √2 2/√3 Not Defined −1 Not Defined 1
This equation is inderminate