How do you prove cosx−(cosx1−tanx)=sinxcosxsinx−cosx?

1 Answer
azturhan
Feb 17, 2016

Please see below for the proof. Feel free to ask questions if you have any.

Explanation:

1) replace tanx with sinxcosx

cosx−(cosx1−tanx)
= cosx−(cosx1−(sinxcosx))

2) equalise the denominator in the paranthesis

= cosx−(cosxcosx−sinxcosx)

=cosx−(cosx⋅cosxcosx−sinx)
=cosx−cos2xcosx−sinx

3) equalise the denominator once more
=cosxcosx−sinxcosx−sinx−cos2xcosx−sinx
=cos2x−cosx⋅sinx−cos2xcosx−sinx
=−(cosx⋅sinx)cosx−sinx

4) put the denominator into -1 paranthesis
=−cosx⋅sinx−(−cosx+sinx)

5) - divided by - yields +. And change the places of cosx and sinx in the denominator

=cosx⋅sinxsinx−cosx

=sinx⋅cosxsinx−cosx

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