Question

(1/(sin^2 alpha) + 1/(cos^2 alpha)) * sin^2 2 * alpha

Помогите пжж!
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Answer 1

Ответ:

$( \frac{1}{ { \sin( \alpha ) }^{2} } + \frac{1}{ { \cos( \alpha ) }^{2} } ) { \sin(2 \alpha ) }^{2} = \\ = ( \frac{2}{1 - \cos(2 \alpha ) } + \frac{2}{1 + \cos(2 \alpha ) } ) { \sin(2 \alpha ) }^{2} = \\ = 2 { \sin(2 \alpha ) }^{2} ( \frac{1 + \cos(2 \alpha ) + 1 - \cos(2 \alpha ) }{1 - { \cos(2 \alpha ) }^{2} } ) = \\ = \frac{4 { \sin(2 \alpha ) }^{2} }{ { \sin(2 \alpha ) }^{2} } = 4$