SOLUTION: Perform each indicated operation and simplify the result cot ϑ + 1/cot ϑ Answer: csc ϑ sec ϑ or 1/sin ϑ cos ϑ how do u find those answers?

Algebra ->  Trigonometry-basics -> SOLUTION: Perform each indicated operation and simplify the result cot ϑ + 1/cot ϑ Answer: csc ϑ sec ϑ or 1/sin ϑ cos ϑ how do u find those answers?      Log On


   

Question 996938: Perform each indicated operation and simplify the result
cot ϑ + 1/cot ϑ
Answer: csc ϑ sec ϑ or 1/sin ϑ cos ϑ
how do u find those answers?
Found 3 solutions by jim_thompson5910, mananth, ikleyn:
Answer by jim_thompson5910(35256) About Me  (Show Source):
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
cottheta%29+ ( 1/cottheta)
=(cot^2theta%29+ 1)/cottheta)
= +sec%5E2%28theta%29+%2Fcot%28theta%29
=1%2Fcos%5E2%28theta%29+%2A+cos%28theta%29%2Fsin%28theta%29
sec%28theta%29%2Acosec%28theta%29

Answer by ikleyn(52782) About Me  (Show Source):
You can put this solution on YOUR website!
.
cot%28theta%29 + 1%2Fcot%28theta%29 = %28cos%28theta%29%29%2Fsin%28theta%29 + 1%2F%28%28cos%28theta%29%29%2F%28sin%28theta%29%29%29 = %28cos%28theta%29%29%2Fsin%28theta%29 + %28sin%28theta%29%29%2F%28cos%28theta%29%29 =     (write it with the common denominator which is sin%28theta%29%2Acos%28theta%29

= %28cos%5E2%28theta%29%29%2F%28sin%28theta%29%2Acos%28theta%29%29 + %28sin%5E2%28theta%29%29%2F%28sin%28theta%29%2Acos%28theta%29%29 = %28sin%5E2%28theta%29+%2B+cos%5E2%28theta%29%29%2F%28sin%28theta%29%2Acos%28theta%29%29 =     (now recall that sin%5E2%28theta%29+%2B+cos%5E2%28theta%29 = 1)

= 1%2F%28sin%28theta%29%2Acos%28theta%29%29.

It is what has to be proved.