Question

Evaluate without using tables sin²60°-1/1-sin60°
a) 1
b) √3/2
c) √2/2
d) 1/2

Answer 1

The evaluation of the given trigonometric expression is -1/4 - sqrt(3)/2.

Step-by-step explanation:

To evaluate the expression sin²60°-1/1-sin60° without using tables, we can use trigonometric identities and properties. First, we know that sin²60° is equal to (sin60°)², which is equal to (sqrt(3)/2)². Next, we can use the identity sin²θ + cos²θ = 1 to simplify the expression even further. Thus, the evaluation is as follows:

sin²60°-1/1-sin60° = (sqrt(3)/2)² - 1/1 - sqrt(3)/2 = 3/4 - 1/1 - sqrt(3)/2 = 3/4 - 4/4 - sqrt(3)/2 = -1/4 - sqrt(3)/2.