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Prove that
Solution:
Consider the given equation above
Rewrite the left side of the equation as a quotient of two trigonometric functions as follows
If
then
Hence, the above equation becomes
Integrate the above equation using the integration of the reciprocal function formula, we have
Note:
because the left side of the equation is a reciprocal of trigonometric function which is equal to sec x while the right side of the equation is inverse trigonometric function which is equal to an angle.
Therefore,
where C is a constant of integration.