Find sinx+cosx if sinx*cosx=3/8

Mathematics

1 answer:

Maurinko [17]3 years ago

5 0

Answer:

$^+_-\frac{\sqrt{7}}{2}.$

Step-by-step explanation:

$1.| \ sinx+cosx| =\sqrt{(sinx+cosx)^2}=\sqrt{sin^2x+2sinxcosx+cos^2x}=\sqrt{1+2sinxcosx};$

2) according to the item 1:

$sinx+cosx=^+_-\sqrt{1+2*\frac{3}{8}} =^+_-\sqrt{\frac{7}{4}}=^+_-\frac{\sqrt{7} }{2}.$

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