Question

Prove that if two angles `alphaandbeta` are complementary angles, then
`cotbeta+cosbeta=(cosbeta)/(cosalpha)(1+sinbeta)`

Answer 1

LHS `=cotbeta+cosbeta=(cosbeta)/(sinbeta)+cosbeta=(cosbeta)/(sin(90^(@)-alpha))+cosbeta`.
`=(cosbeta)/(cosalpha)+cosbeta=(cosbeta)/(cosalpha)(1+cosalpha)`
`=(cosbeta)/(cosalpha){1+cos(90^(@)-beta)}=(cosbeta)/(cosalpha)(1+sinbeta)`
Hence `cotbeta+cosbeta=(cosbeta)/(cosalpha)(1+sinbeta)`.