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:
[tex]\frac{1}{sec^2\theta}[/tex]
Now, sec²θ is also just equivalent to 1/cos²θ. So, we can rewrite the expression as:
[tex]1\div\frac{1}{cos^2\theta}[/tex]
Then, applying the rules of dividing fractions, the expression becomes:
[tex]1\times cos^2\theta=cos^2\theta[/tex]
Therefore, the equivalent expression is cos²θ. (Option 1)
