If cotθ=34then cosec θ=

cotθ=34,θ∈Q1 AC2=AB2+BC2=42+32=16+9=25AC=5cosec2θ−cot2θ=1cot2θ=1+915cosec2θ=1+925=2515cosec2θ−916=1cos2θ=2516

If cotθ=34then cosec θ=

cotθ=34,θ∈Q1 AC2=AB2+BC2=42+32=16+9=25AC=5cosec2θ−cot2θ=1cot2θ=1+915cosec2θ=1+925=2515cosec2θ−916=1cos2θ=2516

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If $c o t θ = \frac{3}{4}$ then $\cos e c θ =$

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$\frac{5}{3}$

$\frac{5}{4}$

$\frac{4}{5}$

$\frac{3}{5}$

answer is B.

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Detailed Solution

$\cot θ = \frac{3}{4}, θ \in Q_{1}$

$A C^{2} = A B^{2} + B C^{2}$

$= 4^{2} + 3^{2}$

$= 16 + 9$

$= 25$

$A C = 5$

$\begin{array}{l} \cos e c^{2} θ - \cot^{2} θ = 1 \\ \cot^{2} θ = 1 + \frac{9}{15} \\ \cos e c^{2} θ = 1 + \frac{9}{25} \\ = \frac{25}{15} \\ \cos e c^{2} θ - \frac{9}{16} = 1 \\ \cos^{2} θ = \frac{25}{16} \end{array}$

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If cotθ=34then cosec θ=

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If $c o t θ = \frac{3}{4}$ then $\cos e c θ =$