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г) ctg(45°-β)/1 - ctg²(45°-β) = ctg 45° × ctgβ +1/ctgβ - ctg 45° / 1 - (ctg 45° × ctgβ +1/ctgβ - ctg 45°)² = cotβ+1/ctgβ-1 / 1-(ctgβ+1/ctgβ-1)² = cotβ+1/ctgβ-1 / 1- (ctgβ+1)²/(ctgβ-1)² = cotβ+1/ctgβ-1 / (ctgβ-1)²-ctg(β+1)²/(ctgβ-1)² = cotβ+1/ctgβ-1 / -2×2ctgβ/(ctgβ-1)² = cotβ+1/ctgβ-1 / -4ctgβ/(ctgβ-1)² = - cotβ+1/ctgβ-1 / 4ctgβ/(ctgβ-1)² = - cotβ+1/ctgβ-1 × (ctgβ-1)²/4ctgβ = - (cotβ+1)×(ctgβ-1)/4ctgβ = - ctg²β-1/4ctgβ = 1-ctg²β/4ctgβ
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б)
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г) ctg(45°-β)/1 - ctg²(45°-β) = ctg 45° × ctgβ +1/ctgβ - ctg 45° / 1 - (ctg 45° × ctgβ +1/ctgβ - ctg 45°)² = cotβ+1/ctgβ-1 / 1-(ctgβ+1/ctgβ-1)² = cotβ+1/ctgβ-1 / 1- (ctgβ+1)²/(ctgβ-1)² = cotβ+1/ctgβ-1 / (ctgβ-1)²-ctg(β+1)²/(ctgβ-1)² = cotβ+1/ctgβ-1 / -2×2ctgβ/(ctgβ-1)² = cotβ+1/ctgβ-1 / -4ctgβ/(ctgβ-1)² = - cotβ+1/ctgβ-1 / 4ctgβ/(ctgβ-1)² = - cotβ+1/ctgβ-1 × (ctgβ-1)²/4ctgβ = - (cotβ+1)×(ctgβ-1)/4ctgβ = - ctg²β-1/4ctgβ = 1-ctg²β/4ctgβ