Question

Evaluate without using tables sin30 + cos^2 60 divided by cos60.

a) 1/2
b) 1
c) √3
d) 2

Answer 1

By using the known values of sin30°, cos60°, and cos^2 60°, the expression simplifies to 1, making the correct answer b) 1.

Step-by-step explanation:

To evaluate sin30 + cos^2 60 divided by cos60, we will use known trigonometric identities and values. The values of sine and cosine at special angles like 30° and 60° are well known. We have:

• sin30° = 1/2
• cos60° = 1/2
• cos^2 60° = (cos60°)^2 = (1/2)^2 = 1/4

Now, plugging in these values, we get:

sin30 + cos^2 60 divided by cos60 = (1/2) + (1/4) ÷ (1/2)

First we need to divide cos^2 60 by cos60:

(1/4) ÷ (1/2) = (1/4) × (2/1) = 1/2

Next, we add this result to sin30:

(1/2) + (1/2) = 1

Therefore, the solution is b) 1.