SOLUTION: what is the simplified form of {{{ cot^2(pi/2 -x)+1

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Question 1133086: what is the simplified form of what+is+the+simplified+form+of+ cot^2(pi/2 -x)+1
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

cot%5E2%28pi%2F2+-x%29%2B1+

start with cot%28pi%2F2+-x%29 first:

since cot%28pi%2F2+-x%29=cos%28pi%2F2+-x%29%2Fsin%28pi%2F2+-x%29

we can use the formulas

cos+%28A-B%29=cos%28A%29cos%28B%29%2Bsin%28A%29sin%28B%29+
and
sin%28A-B%29=sin%28A%29cos%28B%29-cos%28A%29sin%28B%29

then you have



since cos%28pi%2F2%29=0 and sin%28pi%2F2%29=1 we have



cot%28pi%2F2+-x%29=sin%28x%29+%2Fcos%28x%29

cot%28pi%2F2+-x%29=tan%28x%29

then cot%5E2%28pi%2F2+-x%29=tan%5E2%28x%29

and, then cot%5E2%28pi%2F2+-x%29%2B1=tan%5E2%28x%29%2B1