Question

Evaluate;
$\frac{2cos^{2}90 + 4cos^{2}45 + tan^{2} 60 + 3 \cosec^{2} (60) + 1}{3 { \sec}^{2}60 - \frac{7}{2} sec^{2} 45 + 2cosec30 - 1}$

Answer 1

Cos 90° = 0

Cos 45° = 1 / √2

Tan 60° = √3

Cosec 60° = 2 / √3

Sec 60° = 2

Sec 45° = √2

Cosec 30° = 2




$\sf{{\dfrac{2cos^290 \degree + 4cos^245 \degree + tan^260 \degree + 3cosec^260 \degree + 1}{3sec^260 \degree - {\dfrac{7}{2}} sec^245 \degree + 2cosec30 \degree - 1}}}$




Putting values.




$\sf{\implies {\dfrac{2(0)^2 + 4({\dfrac{1}{{\sqrt{2}}}})^2 + ({\sqrt{3}})^2 + 3({\dfrac{2}{{\sqrt{3}}}})^2 + 1}{3(2)^2 - {\dfrac{7}{2}} ({\sqrt{2}})^2 + 2(2) - 1}}}$




$\sf{\implies {\dfrac{2(0) + 4({\dfrac{1}{2}}) + (3) + 3({\dfrac{4}{3}}) + 1}{3(4) - {\dfrac{7}{2}} (2) + 4 - 1}}}$




$\sf{\implies {\dfrac{2 + 3 + 4 + 1}{12 - 7 + 4 - 1}}}$




$\sf{\implies {\dfrac{10}{8}}}$




$\sf\red{\implies {\dfrac{5}{4}}}$

Answer 2

Answer:

$\frac{0 + 2 + 3 + 4 + 1}{6 - 7 + 4 - 1}$

$= \frac{10}{2} = 5$

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