Question #f2c09
3 Answers
Jun 3, 2017
Recall the following identities:
sin2x = sin(x+x) = sinxcosx + cosxsinx
= 2sinxcosx
cos2x = cos(x+x) = cosxcosx - sinxsinx
= cos^2x - sin^2x
sin^2x + cos^2x = 1
This gives:
(2(sinx + cosx))/(2sinxcosx + cos^2x - sin^2x + 1)
= (2(sinx + cosx))/(2sinxcosx + cos^2x - cancel(sin^2x) + cancel(sin^2x) + cos^2x)
= (cancel(2)(sinx + cosx))/(cancel(2)(sinxcosx + cos^2x))
= cancel(sinx + cosx)/(cosxcancel((sinx + cosx)))
= 1/cosx -= color(blue)(secx)
Jun 3, 2017
Proved
Jun 3, 2017
look at picture
Explanation:
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