Verify the identity. 4 csc 2x = 2 csc2x tan x

Step-by-step explanation:

We start with Left hand side

We know that csc(x) = 1/ sin(x)

So csc(2x) is replaced by 1/sin(2x)

Also we use identity

sin(2x) = 2 sin(x) cos(x)

4 divide by 2 is 2

Now we multiply top and bottom by sin(x) because we need tan(x) in our answer

We know that sinx/ cosx = tan(x)

Also  1/ sin(x)= csc(x)

so it becomes 2csc^2(x) tan(x) , Right hand side

Hence verified

452,489 to the nearest thousand is 452,000

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