Question

Which of the following options is equivalent to the given expression (1-sin^(2)(x))/(sin^(2)(x))

a-cosec^(2)(x)
b-sec^(2)(x)
c-cot^(2)(x)
d- tan^(2)(x)

Answer 1

The expression (1 - sin^(2)(x))/(sin^(2)(x))-a-cosec^(2)(x) simplifies to b-sec^(2)(x).

Step-by-step explanation:

The expression (1 - sin^(2)(x))/(sin^(2)(x))-a-cosec^(2)(x) simplifies to b-sec^(2)(x).

To simplify the expression, use the trigonometric identity sin^(2)(x) + cos^(2)(x) = 1. Substitute this identity into the expression:

(1 - sin^(2)(x))/(sin^(2)(x)) = cos^(2)(x)/(sin^(2)(x)) = (1/sin^(2)(x)) * cos^(2)(x)

Since 1/sin(x) = csc(x) and cos^2(x) = 1/sec^2(x), the expression simplifies to b-sec^(2)(x).