Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use for the fraction bar. Simplify the expression. csc²(π/2-x) / 1+tan²(x)

Answer 1

To simplify the expression csc²(π/2-x) / 1+tan²(x), use trigonometric identities to substitute and simplify the expression. The simplified expression is 1.

Step-by-step explanation:

To simplify the expression csc²(π/2-x) / 1+tan²(x), we can use the trigonometric identities:

csc²(x) = 1 + cot²(x)

tan(x) = 1 / cot(x)

Substituting these identities into the expression, we get:

csc²(π/2-x) / 1+tan²(x) = (1 + cot²(π/2-x)) / (1 + (1 / cot(x))²)

Since cot²(π/2-x) = 1 / tan²(x), the expression simplifies to:

(1 + 1 / tan²(x)) / (1 + (1 / cot(x))²)

Simplifying further, we get:

(1 + 1 / tan²(x)) / (1 + 1 / tan²(x)) = 1