Prove:
(cosec theta -sec theta)(cot theta-tan theta)=(cosec theta+sectheta)(sectheta cosectheta-2)
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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
Step-by-step explanation:
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