Question

请问已知sina+cosa=√2，则tana+cota=?

Answer 1

因为 sina+cosa=√2,两边平方
(sina+cosa)²=2
sin²a+2sinacosa+cos²a=2
1+2sinacosa=2
2sinacosa=1
sinacosa=1/2

tana+cota
=sina/cosa+cosa/sina
=(sin²a+cos²a)/(sina*cosa)
=1/(sina*cosa)
=1/(1/2)
=2

Answer 2

sina+cosa=√2 sina=√2-cosa , sin^2a=2-2√2cosa+cos^2a=1-cos^2a
2cos^2a-2√2cosa+1=0 √2cosa=1 , cosa=√2/2, sina=√2/2

tana+cota=sina/cosa+cosa/sina=1/sinacosa=2

Answer 3

(sina+cosa)^2=sina^2+2sina*cosa+cosa^2=1+2sina*cosa=2 ;
sina*cosa=1/2
tana+cota= sina/cosa + cosa/sina = (sina^2+cosa^2)/(sina*cosa)=1/(1/2)=2

Answer 4

2

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