Question 682943
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