How do you verify $sinx + cosx + tanxsinx = secx + cos x tan x$ ?

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Answer 1 · 2016-07-09T00:41:05

Apply the identities $sectheta = 1/costheta$ and $tantheta = sintheta/costheta$ .

$sinx + cosx + sinx/cosx xx sinx = 1/cosx + sinx/cosx xx cosx$

Put on a common denominator:

$(sinxcosx + cos^2x + sin^2x)/cosx = (1 + sinx cosx)/cosx$

Recall that $sin^2beta + cos^2beta = 1$ :

$(1 + sinx cosx)/cosx = (1 + sinx cosx)/cosx$

Hopefully this helps!

How do you verify sinx + cosx + tanxsinx = secx + cos x tan xsinx + cosx + tanxsinx = secx + cos x tan x?