Verify the Identity.

tan²xsin²x = tan²x-sin²x

tan²(x) - sin²(x) = sin²(x)/cos²(x) - sin²(x)

… = sin²(x) (1/cos²(x) - 1)

… = sin²(x) (sec²(x) - 1)

… = sin²(x) tan²(x)

1/5

Step-by-step explanation:

Of the 5 spinner sections, 2 are less than 3.

P(less than 3) = 2/5

Of the 2 sides of the coin, 1 is tails.

P(tails) = 1/2

The compound probability is therefore:

P = 2/5 × 1/2

P = 1/5