Question

If cosecθ = √2, then find the value of 2sin²θ+3cot²θ/4tan²θ-cos²θ

Answer 1

$\cosec \theta = \sqrt{2} \\ \\ \cosec \theta = \cosec30$



Hence,


$\frac{2 \sin ^{2} \theta+ 3 { \cot }^{2} \theta}{4 \tan ^{2} \theta - { \cos }^{2} \theta }$



$=> \frac{ [ 2 \times ( \frac{1}{2})^{2} ) ] + [ 3 \times ( \sqrt{3} )^{2} ] }{ [ 4 \times ( \frac{1}{ \sqrt{3}} )^{2} ] - [ \frac{\sqrt{3}}{2} ]^{2} }\\ \\ \\ => \frac{ \frac{1}{2 } + 9}{ \frac{4}{3} - \frac{3}{4} } \\ \\ \\ = > \frac{ \frac{1 + 18}{2} }{ \frac{16 - 9}{12} } \\ \\ \\ = > \frac{19}{2} \times \frac{12}{7} \\ \\ \\ = > \frac{19 \times 6}{7} \\ \\ \\ = > \frac{114}{7}$

Answer 2

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