Video Transcript
Simplify sin π multiplied by csc
π minus cos squared π.
In this question, we are asked to
simplify a trigonometric expression. One way of doing this is using the
reciprocal and Pythagorean identities. In questions of this type, it is
not always clear what to do first. However, as a general rule, it is
worth replacing any reciprocal functions with the sine, cosine, or tangent
function.
We know that csc π is equal to one
over sin π. Substituting this into our
expression, we have sin π multiplied by one over sin π minus cos squared π. The sin π on the numerator and
denominator of our first term cancels, leaving us with one minus cos squared π. Next, we recall one of the
Pythagorean identities: sin squared π plus cos squared π is equal to one. Subtracting cos squared π from
both sides, this can be rewritten as sin squared π is equal to one minus cos
squared π. This means that our expression can
be rewritten as sin squared π. sin π multiplied by csc π minus
cos squared π written in its simplest form is sin squared π.
