[latex] \dfrac{\text{15}\left({\text{sin}}^{2}{\text{21}}^{o}{\text{-cos}}^{2}{\text{21}}^{o}\right)}{\text{cos4}{2}^{o}} [/latex]

Question

[latex] \dfrac{\text{15}\left({\text{sin}}^{2}{\text{21}}^{o}{\text{-cos}}^{2}{\text{21}}^{o}\right)}{\text{cos4}{2}^{o}} [/latex]

Гость

Ответ(ы) на вопрос:

Гость

[latex]cos42=cos^{2}21-sin ^{2} 21; \frac{15( sin^{2}21- cos^{2}21)}{ cos42} = \frac{-15( cos^{2}21- sin^{2}21)}{ cos42}=[/latex] = -15cos42 / cos42 = -15

Accepted Answer

[latex] \frac{15*(sin^{2}21^{0} -cos^{2}21 ^{0} )}{cos42^{0} } = \frac{15*(-(cos^{2} 21 ^{0}-sin^{2} 21 ^{0} ))}{cos42 ^{0} }= \frac{-15*cos(2*21^{0} )}{cos42^{0} } = [/latex] [latex]= \frac{15cos42 ^{0} }{cos42 ^{0} } =-15[/latex]