Question

please help... class 10th Maths​

Answer 1

Question :-

Evaluate :

$\sf\frac{5 { \cos }^{2} 60° \: + \: 4 { \sec }^{2}30°\: - \: \tan ^{2}45° } { { \sin }^{2} 30° \: + \: \cos^{2}30° }$

Solution :-

$\implies\:$$\sf\frac{5 { \cos }^{2} 60° \: + \: 4 { \sec }^{2}30°\: - \: \tan ^{2}45° } { { \sin }^{2} 30° \: + \: \cos^{2}30° }$

$\implies\:$ $\sf\frac{5 {( \frac{1}{2} )}^{2} \: + \: 4 {( \frac{2}{3}) }^{2} - 1}{1}$

$\implies\:$ $\sf\frac{5}{4} + \frac{16}{3} - 1$

$\implies\:$ $\sf\frac{15 + 64 - 12}{12}$

$\implies\:$ $\sf\frac{67}{12}$

Answer 2

${ \tt{ \large \pink{question \colon}}}$

${ \rm{\dfrac{5 {cos}^{2} 60 \degree + 4 {sec}^{2}30 \degree - {tan}^{2} 45 \degree}{ {sin}^{2} 30 \degree + {cos}^{2} 30 \degree} }}$

${ \tt{ \large \pink{solution \colon}}}$

${ \rm{\dfrac{5 {cos}^{2} 60 \degree + 4 {sec}^{2}30 \degree - {tan}^{2} 45 \degree}{ {sin}^{2} 30 \degree + {cos}^{2} 30 \degree} }}$

${ \rm{ = \dfrac{5 ( { \frac{1}{2}) }^{2} + 4 ({ \frac{2}{ \sqrt{3} } )}^{2} - 1}{ ({ \frac{1}{2}) }^{2} + ({ \frac{ \sqrt{3} }{2}) }^{2} } }}$

${ \rm{ = \dfrac{5 ( { \frac{1}{4}) } + 4 ({ \frac{4}{ 3} )} - 1}{ ({ \frac{1}{4}) } + ({ \frac{ 3}{4}) }} }}$

${ \rm{ = \dfrac{{ \frac{5}{4} } + { \frac{16}{ 3} } - 1}{ { \frac{1}{4} } + { \frac{ 3}{4} }} }}$

${ \rm{ = \dfrac{ \dfrac{15 + 64 - 12}{12} }{ \dfrac{1 + 3}{4} } }}$

${ \rm{ = \dfrac{ \dfrac{91}{12} }{ \dfrac{ \not4}{ \not4} } }}$

${ \rm{ = \dfrac{67}{12} = 5.583 }}$

${ \rm{ = 5.583}}$