Question

Sin B ( sin B + cot B ) = 1 + cos A - cos^2 A ?

Answer 1

`Sin B ( sin B + cot B ) = 1 + cos B - cos^2 B`
`sin^2B+cosB/cancel(sinB)*cancel(sinB)= 1 + cos B - cos^2 B`
`sin^2B+ cosB= 1 + cos B - cos^2 B`
Manipulated Pythagorean identity:
`1-cos^2x= sin^2x`
Substitute `1-cos^2x` for `sin^2x`
`(1-cos^2x)+ cosB= 1 + cos B - cos^2 B`
`1 + cos B - cos^2 B= 1 + cos B - cos^2 B`