Verify the identity.

4 csc 2x = 2 csc^2x tan x

To verify the given identity, we work with the value on the right hand side. That is:

2 (csc^2 (x)) (tan x)

We know that csc is the inverse of sine and that tan = sin / tan, therefore:

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

Cancelling sin x:

= 2 (1 / sin x) (1 / cos x)

Multiplying both the numerator and denominator by 2:

= 4 / 2 sin x cos x

From the trigonometric identities, 2 sin x cos x = sin 2x, therefore:

= 4 / sin 2x

= 4 csc 2x

Hence, it is proven.

step-by-step explanation:

your mom

percentage - 25%

probability - 0.25

we know,

total amount of students in class = 20

total boys = 10

total girls = 10

no of girls who wear glasses = 10/2 = 5

probability of choosing a girl with glasses is =

number of girls wearing glasses/total number of students in the class = 5/20

thus, percentage of selecting a girl wearing glasses will be

= 5/20 × 100

= 5 × 5

25%

therefore,

probability will be 0.25

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