Question

Hello! Can u answer this question??

Answer 1

$\boxed{ \huge \mathfrak{solution}}$

To find :

The value :

$\star \: \boxed{ \bold{ \frac{7}{ {cot}^{2} \phi } - \frac{7}{ {cos}^{2} \phi } }}$

$\rightarrow \: 7( \frac{1}{ {cot}^{2} \phi } - \frac{1}{ {cos}^{2} \phi} ) \\ \\ \rightarrow \: 7( \frac{1}{ \frac{ {cos}^{2} \phi}{ {sin}^{2} \phi } } - \frac{1}{ {cos}^{2} \phi} ) \\ \\ \rightarrow \: 7( \frac{ {sin}^{2} \phi}{ {cos}^{2} \phi } - \frac{1}{ {cos}^{2} \phi} ) \\ \\ \rightarrow \: 7( \frac{ {sin}^{2} \phi - 1 }{ {cos}^{2} \phi } ) \\ \\ \rightarrow \: 7 \cancel{( \frac{ - {cos}^{2} \phi }{ {cos}^{2} \phi} )} \\ \\ \rightarrow \: - 7$

Option :

$\huge\boxed{ \red{D ) - 7</p><p>}}$

Answer 2

$\huge{\pink{\underline{\black{\mathbb{Trigonometry}}}}}$

$\frac{7}{ \cot {}^{2} (x) } - \frac{7}{ \cos {}^{2} (x) }$

$= 7( \frac{ \sin {}^{2} x) }{ \cos {}^{2} (x) } - \frac{1}{ \cos {}^{2} (x) } )$

$= 7 \frac{( \sin {}^{2} (x) - 1 )}{ \cos {}^{2} (x) }$

we know that

sin² x+ cos²x = 1

then ,

$= 7 \frac{ \ (- cos {}^{2} (x)) }{ \cos {}^{2} (x) }$

$= - 7$