Question

cosecQ +cotQ=1/3 then find cosQ

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Answer 1

Step-by-step explanation:

$(CosecQ + CotQ) =\frac{1}{3}$ ----(1)

$Cose²Q - Cot²Q = 1$

$(CosecQ+CotQ)(CosecQ-CotQ)=1$

$\frac{1}{3}(CosecQ-CotQ)=1$

$(CosecQ - CotQ) = 3$ -----(2)

$From \: eq.(1) + eq.(2)-$

$2CosecQ =(\frac{1}{3} + 3)$

$2CosecQ =(\frac{10}{3})$

$CosecQ =\frac{5}{3}$

$then , SinQ =\frac{3}{5}$

$Now , CosQ =\sqrt{(1-Sin²Q)}$

$CosQ =\sqrt{(1 - \frac{9}{25})}$

$CosQ =\sqrt{(\frac{16}{25})}$

$CosQ =\frac{4}{5}$