prove that sintheta(1+tantheta)+costheta(1+cottheta)=sectheta+cosectheta

Asked by riyaliz | 17th Jul, 2008, 01:20: AM

Expert Answer:

sinθ(1+tanθ) +cosθ(1+cotθ)

= sinθ(1+sinθ/cosθ) + cosθ(1+cosθ/sinθ)

= (sinθ/cosθ)(sinθ+cosθ) + (cosθ/sinθ)(sinθ+cosθ)

= (sinθ+cosθ)(sinθ/cosθ + cosθ/sinθ)

= (sinθ+cosθ)(1/sinθcosθ)

= secθ+cosecθ

Answered by  | 17th Jul, 2008, 12:06: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.