Question

Помогите вычислить :::

Answer 1

$\frac{cos76 - cos16}{1 - {sin}^{2}22 } = \frac{ - 2 \sin( \frac{76 + 16}{2} ) \sin( \frac{76 - 16}{2} ) }{ {cos}^{2} 22} = \frac{ - 2 \sin(46) \sin(30) }{ {cos}^{2} 22} = \frac{ - 2 \sin(90 - 44) \times \frac{1}{2} }{ {cos}^{2}22 } = \frac{ - cos44}{ {cos}^{2} 22} = - \frac{ {cos}^{2}22 - {sin}^{2} 22}{ {cos}^{2} 22} = - (1 - {tg}^{2} 22) = - 1 + {tg}^{2} 22$