Question

Evaluate till the end

Answer 1

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\frac{tan^{2}\:60\degree+4\:cos^{2}\:45\degree+3\:sec^{2}\:30\degree+5\:cos^{2}\:90\degree}{cosec\:30\degree+sec\:60\degree-cot^{2}\:30\degree=15}}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\underline \bold{To \: Find : } \\ \implies \frac{tan^{2} 60 \degree + 4 cos ^{2}45 \degree + 3 \: sec ^{2} 30 \degree + 5 \: {cos}^{2} 90 \degree}{ {cosec} \: 30 \degree + {sec} \: 60 \degree - {cot}^{2} 30 \degree} = ?$

• According to given question :

$\circ{ \: \: tan \: 60 \degree = \sqrt{3} } \\ \\ \circ{ \: \: cos\: 45 \degree = \frac{1}{ \sqrt{2} } } \\ \\ \circ{ \: \:sec \: 30\degree = \frac{2}{ \sqrt{3} } } \\ \\ \circ{ \: \: cos \: 90\degree = 0} \\ \\ \circ{ \: \: cosec \: 30 \degree = 2 } \\ \\ \circ{ \: \: sec\: 60 \degree = 2 } \\ \\ \circ{ \: \: cot\: 30\degree = \sqrt{3} } \\ \\ \bold{substituting \: values \: given \: above : } \\ \implies \frac{tan^{2} 60 \degree + 4 \: cos ^{2}45 \degree + 3 \: sec ^{2} 30 \degree + 5 \: {cos}^{2} 90 \degree}{ {cosec} \: 30 \degree + {sec} \: 60 \degree - {cot}^{2} \: 30 \degree} \\ \\ \implies \frac{ ({ \sqrt{3} })^{2} + 4 \times (\sqrt{2})^{2} + 3 \times (\frac{2}{ \sqrt{3} }) ^{2} + 5 \times 0 }{2 + 2 - ( \sqrt{3} )^{2} } \\ \\ \implies \frac{3 + 4 \times 2 + 3 \times \frac{4}{3} + 0}{4 - 3} \\ \\ \implies \frac{3 + 8 + 4}{1} \\ \\ \bold{\implies 15}$

Answer 2

$\implies \frac{tan^{2} 60 \degree + 4 \: cos ^{2}45 \degree + 3 \: sec ^{2} 30 \degree + 5 \: {cos}^{2} 90 \degree}{ {cosec} \: 30 \degree + {sec} \: 60 \degree - {cot}^{2} \: 30 \degree} \\ \\ \implies \frac{ ({ \sqrt{3} })^{2} + 4 \times (\sqrt{2})^{2} + 3 \times (\frac{2}{ \sqrt{3} }) ^{2} + 5 \times 0 }{2 + 2 - ( \sqrt{3} )^{2} } \\ \\ \implies \frac{3 + 4 \times 2 + 3 \times \frac{4}{3} + 0}{4 - 3} \\ \\ \implies \frac{3 + 8 + 4}{1} \\ \\ \bold{\implies 15}$