# Video: Evaluating Trigonometric Expressions Using Reciprocal Identities

Find the value of 2 sin π csc π +11 cos π sec π + 7 tan π cot π.

01:48

### Video Transcript

Find the value of two sin π csc π plus 11 cos π sec π plus seven tan π cot π.

To solve this problem, we need to recognize reciprocal identities. First, letβs think about ways we can rewrite cosecant, secant, and cotangent. Csc is equal to one over sin π. Sec π is one over cos π. And cot π is equal to one over tan π. What does this mean? Well, one over sin π is the reciprocal of sin π. And that means cosecant is the reciprocal of sine. It means that sec π is the reciprocal of cos π, and that cotangent is the reciprocal of tangent.

If we multiply sin π by its reciprocal, one over sin π, weβll get sin π over sin π, which is one. Anything multiplied by its reciprocal is one. Two times sin π times csc π is equal to two times one. The same thing is true for cos π times sec π. Cos π times its reciprocal equals one. And so, the second term will be 11 times one. Tan π times its reciprocal equals one. And so, our third term will be seven times one. We can simplify this expression to, say, two plus 11 plus seven, which equals 20.