Question

Can you help me with this? Also the word at the beginning is what. It is the only thing that got cut off.

Answer 1

To be able to simplify the given expression, let's recall some of the trigonometric identities.

1. sin²θ + cos²θ = 1

2. 1 + tan²θ = sec²θ

From those identities above, we can replace the numerator and denominator in the given expression with their equivalent value. Thus, the expression becomes:

`(1)/(sec^2\theta)`

Now, sec²θ is also just equivalent to 1/cos²θ. So, we can rewrite the expression as:

`1/(1)/(cos^2\theta)`

Then, applying the rules of dividing fractions, the expression becomes:

`1* cos^2\theta=cos^2\theta`

Therefore, the equivalent expression is cos²θ. (Option 1)