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
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