Question

ТРИГОНОМЕТРІЯ.будь ласка 1 завдання

Answer 1

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