Question

Sabendo que cos x = 0,25, determine o valor da expressão:

( sec x * cossec x - sec² x ) / ( cotg x - 1 )

Resposta: 16

Answer 1

Olá Alisson!

$\\ \displaystyle \mathsf{\frac{\sec x \cdot \csc x - \sec^2 x}{\cot x - 1} =} \\\\\\ \mathsf{\left ( \frac{1}{\cos x} \cdot \frac{1}{\sin x} - \frac{1}{\cos^2 x} \right ) \div \left ( \frac{\cos x}{\sin x} - 1 \right ) =} \\\\\\ \mathsf{\left ( \frac{\cos x - \sin x}{\cos^2 x \cdot \sin x} \right ) \div \left ( \frac{\cos x - \sin x}{\sin x} \right ) =} \\\\\\ \mathsf{\frac{\cos x - \sin x}{\cos^2 x \cdot \sin x} \cdot \frac{\sin x}{\cos x - \sin x} =}$

$\\ \displaystyle \mathsf{\frac{1}{\cos^2 x \cdot 1} \cdot \frac{1}{1} =} \\\\\\ \mathsf{\frac{1}{\cos^2 x} =} \\\\\\ \mathsf{\left ( \frac{1}{\cos x} \right )^2 =} \\\\\\ \mathsf{\left ( \frac{1}{0,25} \right )^2 =} \\\\\\ \mathsf{\left ( 1 \div \frac{25}{100} \right )^2 =} \\\\\\ \mathsf{(4)^2 =} \\\\ \boxed{\boxed{\mathsf{16}}}$