Question

Тригонометрия. 40 баллов.
26cos^2 a-1 при tg a=1/5
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Answer 1

$tga=frac{1}{5}\\26cos^2a-1=26cdot frac{1+cos2a}{2}-1=13cdot (1+cos2a)-1=13cdot cos2a+12=\\=13cdot frac{1-tg^2a}{1+tg^2a}+12=13cdot frac{1-frac{1}{25}}{1+frac{1}{25}}+12=13cdot frac{24}{26}+12=frac{24}{2}+12=12+12=24\\\Formylu:\\star ; ; cos^2x=frac{1+cos2x}{2}; ; star \\star ; ; cos2x=cos^2x-sin^2x=frac{cos^2x-sin^2x}{cos^2x+sin^2x}=[, frac{:cos^2x}{:cos^2x}, ]=frac{1-tg^2x}{1+tg^2x}; ; star$