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Prove that
Solution:
Consider the given equation above
In proving the trigonometric identities, we have to choose the more complicated part which is the left side of the equation. We have to use the principles of simplifying trigonometric functions as much as we can until we get the same equation as the right side of the equation. Let's rewrite the trigonometric functions of negative angles into its equivalent trigonometric functions of positive angles as follows
If an angle is negative, then it is located in the fourth quadrant. The negative angle is measured in a clockwise direction. Sine is negative, cosine is positive, tangent is negative, cosecant is negative, secant is positive, and cotangent is negative in the fourth quadrant. Hence, the above equation becomes
Take out the negative signs at the left side of the equation, we have
Rewrite the rational and reciprocal functions as follows
but
Hence the above equation becomes
Therefore,
