tanа=1/2,则(sinа+cosа)²/cos2а等于多少?

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tanа=1/2,则(sinа+cosа)²/cos2а等于多少?

tanа=1/2,则(sinа+cosа)²/cos2а等于多少?
tanа=1/2,则(sinа+cosа)²/cos2а等于多少?

tanа=1/2,则(sinа+cosа)²/cos2а等于多少?
(sinа+cosа)²/cos2а
= (sin²a+2sina·cosa+cos²a)/(cos²-sin²a)
= (tan²a+2tan a+1)/(1-tan²a) 【分子分母同除以cos²a】
= (1/4+2·1/2+1)/(1-1/4)
= (9/4)/(3/4)
= 3

(sinа+cosа)²/cos2а
= sin²а+2sinаcosа+cos²а/cos2а
= 1+2sinаcosа/cos2а
= 1+sin2а/cos2а
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