Find the actual value of

Cosec60×cot60/sec45/cos30 by showing all your working out

see your previous posts and work this the same way. We can check your answer.

√6/6

To find the actual value of the given expression, let's break it down step by step and simplify each part:

1. First, let's evaluate cosec60 and cot60.
The reciprocal of sine is known as the cosecant function, so we have cosec60 = 1/sin60.
In a right triangle with a 60-degree angle, the side opposite the 60-degree angle is √3 times the length of the shorter side. Therefore, sin60 = √3/2.
Substituting this value, we get cosec60 = 1/(√3/2) = 2/√3.

Cotangent is the reciprocal of the tangent function, so cot60 = 1/tan60.
In a right triangle with a 60-degree angle, the side opposite the 60-degree angle is √3 times the length of the shorter side, and the adjacent side is equal to the shorter side. Hence, tan60 = √3.
Substituting this value, we get cot60 = 1/√3 = √3/3.

2. Next, let's evaluate sec45 and cos30.
The reciprocal of cosine is known as the secant function, so we have sec45 = 1/cos45.
In a right triangle with a 45-degree angle, the legs are equal, so cos45 = √2/2.
Substituting this value, we get sec45 = 1/(√2/2) = 2/√2 = √2.

Cosine of 30 degrees is √3/2.

3. Now, substitute all the simplified values back into the expression:
Cosec60 × cot60 / sec45 / cos30
= (2/√3) × (√3/3) / √2 / (√3/2)
= 2/(√3) × (√3/3) × 2/(√2) × (2/√3)
= 4 / (√3 × 3) × 2 / (√2 × √3)
= 4 / (3√3) × 2 / (√6)
= 8 / (3√3 × √6)
= 8 / (√18 × √3)
= 8 / √(18 × 3)
= 8 / √54
= 8 / (√(9 × 6))
= 8 / (3√6)

Therefore, the actual value of Cosec60 × cot60 / sec45 / cos30 is 8 / (3√6).