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astghikm
@astghikm
August 2021
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kalbim
Verified answer
tg(x/2) = sinx/(1 + cosx)
tg((π/4)/2) = (1 - cos(π/4))/sin(π/4) = (1 - √2/2) / √2/2 = (2 - √2)/√2 = √2 - 1
ctg(π/8) = 1/tg(π/8) = 1/(√2 - 1) = (√2 + 1)/(2 - 1) = √2 + 1
√2 - 1 + √2 + 1 = 2√2
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astghikm
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Answers & Comments
Verified answer
tg(x/2) = sinx/(1 + cosx)tg((π/4)/2) = (1 - cos(π/4))/sin(π/4) = (1 - √2/2) / √2/2 = (2 - √2)/√2 = √2 - 1
ctg(π/8) = 1/tg(π/8) = 1/(√2 - 1) = (√2 + 1)/(2 - 1) = √2 + 1
√2 - 1 + √2 + 1 = 2√2