Question

Помогите вычислить :::

Answer 1

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