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Question
Prove the following identity :
`sinθ(1 + tanθ) + cosθ(1 +cotθ) = secθ + cosecθ`
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Solution
`sinθ(1 + tanθ) + cosθ(1 +cotθ) = secθ + cosecθ`
LHS = `sinθ(1 + tanθ) + cosθ(1 + cotθ)`
= `sinθ (1 + sinθ/cosθ) + cosθ (1 + cosθ /sinθ)`
= `sinθ((cosθ + sinθ)/cosθ) + cosθ((sinθ + cosθ)/sinθ)`
= `cosθ + sinθ(sinθ /cosθ + cosθ /sinθ)`
= `cosθ + sinθ (1/sinθ 1/cosθ) = secθ + cosecθ `
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