Question
Hello!
In order to prevent confusion that may be caused by reading this problem written through keyboard text, I have written the identity in microsoft paint here:
gyazo. com/d4529f091e5ba75c09a9a283201504d2
I need to find three different ways (Different meaning beginning each proof with a different strategy such as "multiply by conjugate") to prove that this identity is correct, but anything less than that is appreciated! Cheers
In order to prevent confusion that may be caused by reading this problem written through keyboard text, I have written the identity in microsoft paint here:
gyazo. com/d4529f091e5ba75c09a9a283201504d2
I need to find three different ways (Different meaning beginning each proof with a different strategy such as "multiply by conjugate") to prove that this identity is correct, but anything less than that is appreciated! Cheers
Answers
Steve
sin/(1-cos/sin) + cos/(1-sin/cos)
= sin/((sin-cos)/sin) + cos/((cos-sin)/cos)
= sin^2/(sin-cos) + cos^2/(cos-sin)
= (sin^2-cos^2)/(sin-cos)
= (sin-cos)(sin+cos)/(sin-cos)
= sin+cos
gotta run -- maybe more later
= sin/((sin-cos)/sin) + cos/((cos-sin)/cos)
= sin^2/(sin-cos) + cos^2/(cos-sin)
= (sin^2-cos^2)/(sin-cos)
= (sin-cos)(sin+cos)/(sin-cos)
= sin+cos
gotta run -- maybe more later