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How do you prove (sinx)(cosx)(tanx) + cos2x = 1 ?

Answer 1

Samantha Abate

We have:

#sinx(cosx)(sinx/cosx) + cos(2x) = 1#

#sin^2x + 1 - 2sin^2x = 1#

#-sin^2x = 0#

#sinx = 0#

#x = 0 or pi ->x= pin#

Hopefully this helps!

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Answer 2

Oliver Atkinson

#f(x) = (sin x)(cos x) (sin x/cos x) + cos 2x =# #= sin^2 x + cos 2x#. Replace cos 2x by #(cos^2 x - sin^2 x)# #f(x) = sin^2 x + cos^2 x - sin^2 x = cos^2 x# The equation #f(x) = cos^2 x = 1# is impossible, except when #cos^2 x = 1# --> #cos x = +- 1# --> #x = kpi#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.