SOLUTION: I need help slove this identity, please show the steps becasue I subed in 2 for B and both sides were the same so I know it is an identity but I do not how to prove it without subi

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Question 682943: I need help slove this identity, please show the steps becasue I subed in 2 for B and both sides were the same so I know it is an identity but I do not how to prove it without subing in a number
(1+2inBcosB)/(sinB+cosB)=sinB+cosB
Thanks :)
Found 2 solutions by mananth, lwsshak3:
Answer by mananth(16946) About Me  (Show Source):
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
prove following identity:
(1+2sinBcosB)/(sinB+cosB)=sinB+cosB
start with left side
(1+2sinBcosB)/(sinB+cosB)
multiply top and bottom by (sinB+cosB)
=(1+2inBcosB)/(sinB+cosB)* (sinB+cosB)/ (sinB+cosB)
=(1+2inBcosB)(sinB+cosB/ (sinB+cosB)/ (sinB+cosB)
=(1+2inBcosB)(sinB+cosB/ (sin^2B+2sinBcosB+cos^2B)
=(1+2inBcosB)(sinB+cosB/ (1+2sinBcosB)
=sinB+cosB
verified:
left side=right side