Find the actual value of
Cos45×cot30-sec60 by showing all your working out
see your previous two posts and work this the same way. We can check your answer.
-4+√6/2
To find the actual value of the expression, let's break it down step by step:
1. Cosine of 45 degrees: Start by finding the value of cos(45°). Cosine refers to the ratio of the adjacent side length to the hypotenuse in a right triangle. Since we know that a 45-45-90 degree triangle is an isosceles right triangle, we can use the property that the two shorter sides are equal. In this case, the adjacent side and the opposite side are both of length 1. Therefore, cos(45°) = adjacent/hypotenuse = 1/√2 = √2/2.
2. Cotangent of 30 degrees: Next, let's calculate cot(30°). Cotangent is the reciprocal of the tangent and is equal to the ratio of the adjacent side to the opposite side in a right triangle. For a 30-60-90 degree triangle, the ratio of the opposite side to the adjacent side is √3/1. Thus, cot(30°) = adjacent/opposite = 1/(√3/3) = √3/3.
3. Secant of 60 degrees: The secant of an angle is the reciprocal of the cosine and is equal to the ratio of the hypotenuse to the adjacent side in a right triangle. In a 30-60-90 triangle, the ratio of the hypotenuse to the adjacent side is 2. Therefore, sec(60°) = hypotenuse/adjacent = 2/1 = 2.
Now, we can substitute the calculated values back into the expression and solve:
cos(45°) × cot(30°) - sec(60°)
= (√2/2) × (√3/3) - 2
= (√6/6) - 2
= (√6 - 12)/6
So, the actual value of cos(45°) × cot(30°) - sec(60°) is (√6 - 12)/6.