Verify the identity .
(cscX-cotX)^2=1-cosX/1+cosX
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sorry i cant help you
(cscX-cotX)=1/sinX - cosX/sinX = (1-cosX)/sinX
If you square this you have (1-cosX)^2/(sinX)^2
Now use (sinX)^2 = 1 - (cosX)^2 to get
(1-cosX)^2 / 1 - (cosX)^2 =
[(1-cosX)*(1-cosX)]/[(1 - cosX)*(1 + cosX)
Then simplify.
To verify the identity, we need to simplify both sides and show that they are equal.
Starting with the left side of the equation:
(cscX - cotX)^2 = [(1 - cosX)/(sinX)]^2
Expanding the square:
[(1 - cosX)/(sinX)]^2 = [(1 - cosX)^2]/(sinX)^2
Using the identity (sinX)^2 = 1 - (cosX)^2, we substitute the value:
[(1 - cosX)^2]/(1 - (cosX)^2)
Now, let's simplify the right side of the equation:
1 - cosX / 1 + cosX
To combine the fractions, we need a common denominator:
(1 - cosX)(1 - cosX) / (1 - cosX)(1 + cosX)
Now, cancel out the common factors:
(1 - cosX) / (1 + cosX)
Therefore, we have shown that the left side [(1 - cosX)^2]/(1 - (cosX)^2) is equal to the right side (1 - cosX) / (1 + cosX). Hence, the identity is verified.