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CBSE Class 10 Answered

prove that sintheta(1+tantheta)+costheta(1+cottheta)=sectheta+cosectheta
Asked by riyaliz | 17 Jul, 2008, 01:20: AM
answered-by-expert 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 | 17 Jul, 2008, 12:06: PM
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