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Find the value SinQ (1 + tanQ) + CosQ (1 + CotQ)?

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SecQ + CosecQ

SecQ - CosecQ

SecQ - SinQ

Sin²Q - Cos²Q

answer is A.

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Detailed Solution

⇒SinQ (1 + tanQ) + CosQ (1 + CotQ)
⇒SinQ (1 +

\frac{SinQ}{CosQ}) + CosQ (1 + \frac{CosQ}{SinQ})

⇒SinQ +

\frac{Sin²Q}{CosQ} + CosQ + \frac{Cos²Q}{SinQ}

⇒(SinQ +

\frac{Co s^{2} Q}{SinQ}) + (CosQ + \frac{Si n^{2} Q}{CosQ})

\Rightarrow \frac{Si n^{2} Q + Co s^{2} Q}{SinQ} + \frac{Cos²Q + Sin²Q}{CosQ}

⇒

(\frac{1}{SinQ} + \frac{1}{CosQ})

= (SecQ + CosecQ)

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