Prove that: sin θ (1 + tan θ) + cos θ (1 + cot θ) = sec θ + cosec θ

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Prove that: sin θ (1 + tan θ) + cos θ (1 + cot θ) = sec θ + cosec θ
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Prove that: sin A (1 + tan A) + cos A (1 + cot A) = sec A+ cosec A
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