Question
Verify:
Tan u + sec u-1 / tan u - sec u+1 = tan u + sec u
Tan u + sec u-1 / tan u - sec u+1 = tan u + sec u
Answers
Steve
You have
(tan+sec-1)/(tan-(sec-1))
multiply top and bottom by tan+sec-1 and you have
(tan+sec-1)^2/(tan^2-(sec-1)^2)
tan^2+sec^2+1+2tan*sec-2tan-2sec)/(tan^2-sec^2+2sec-1)
(sec^2+tan*sec-tan-sec)/(sec-1)
(tan+sec)(sec-1)/(sec-1)
tan+sec
(tan+sec-1)/(tan-(sec-1))
multiply top and bottom by tan+sec-1 and you have
(tan+sec-1)^2/(tan^2-(sec-1)^2)
tan^2+sec^2+1+2tan*sec-2tan-2sec)/(tan^2-sec^2+2sec-1)
(sec^2+tan*sec-tan-sec)/(sec-1)
(tan+sec)(sec-1)/(sec-1)
tan+sec
Anonymous
Two steps after multiplying the top and bottom, why does tan become 2tan on top
Steve
tan does not become 2tan
expand (a+b-1)^2 and you will see the 2's, just as
(a+b)^2 = a^2 + 2ab + b^2
expand (a+b-1)^2 and you will see the 2's, just as
(a+b)^2 = a^2 + 2ab + b^2