Question

Simplify the expression sin ²θ/ cos ² θ.

A) tan ²θ
B) sec ²θ
C) csc ²θ .
D) cot ²θ

Answer 1

To simplify the expression sin ²θ/ cos ² θ, we can use the trigonometric identity sin²θ = 1 - cos²θ. Substituting this into the expression and simplifying, we get sec²θ as the final result.

Step-by-step explanation:

To simplify the expression sin ²θ/ cos ² θ, we can use the trigonometric identity:

sin²θ = 1 - cos²θ

Substituting this into the expression, we get:

sin ²θ/ cos ² θ = (1 - cos²θ)/ cos ² θ

Next, we can simplify this by factoring out the common term cos²θ:

(1 - cos²θ) / cos ² θ= (1/cos²θ - cos²θ/ cos²θ)

Finally, we can simplify further and obtain:

1/cos²θ - cos²θ/ cos²θ = sec²θ - 1 = sec²θ - sec²θ + tan²θ

Therefore, the simplified expression is B) sec ²θ.