Question

Verify that question ​

Answer 1

Question :-

Verify it .

$\sf4 { \cot}^{2} 30 \degree + 9 { \sin}^{2} 60 \degree - 6 { \csc}^{2} 60 \degree - \frac{9}{4} { \tan}^{2}60 \degree = 4$

Used values :-

$\star \: \cot30 \degree = \sqrt{3} \\ \\ \star \sin60 \degree = \frac{ \sqrt{3} }{2} \\ \\ \star \: \csc60 \degree = \frac{2}{ \sqrt{3} } \\ \\ \star \tan60 \degree = \sqrt{3}$

Explanation :-

We have ,

$\sf4 { \cot}^{2} 30 \degree + 9 { \sin}^{2} 60 \degree - 6 { \csc}^{2} 60 \degree - \frac{9}{4} { \tan}^{2}60 \degree \: \\ \\ \rightarrow \: 4 { ({ \sqrt{3} }) }^{2} + 9 {( \frac{ \sqrt{3} }{2}) }^{2} - 6 {( \frac{2}{ \sqrt{3} }) }^{2} - \frac{9}{4} {( \sqrt{3} )}^{2} \\ \\ \rightarrow 12 + \frac{9 \times 3}{4} - \frac{6 \times 4}{3} - \frac{9 \times 3}{4} \\ \\ \rightarrow \: \:12 - \frac{24}{3} \\ \\ \rightarrow \: \frac{36 - 24}{3} \\ \\ \rightarrow \: \frac{12}{3} = 4$

hence verified.