How do you show tanx/tanx+sinx = 1/1+cosx?

How can I show that #tanx/(tanx+sinx) = 1/(1+cosx)#
Not quite too sure in how to answer these questions

2 Answers
Abhishek K.
Mar 10, 2018

#LHS=tanx/(tanx+sinx)#

#=cancel(tanx)/(cancel(tanx)(1+sinx/tanx))#

#=1/(1+sinx*cosx/sinx)=1/(1+cosx)=RHS#

maganbhai P.
Mar 10, 2018

Please see explanation.

Explanation:

Here,
#tanx/(tanx+sinx)=1/(1+cosx)#
#LHS=tanx/(tanx+sinx)=(sinx/cosx)/(sinx/cosx+sinx#
#LHS=sinx/(sinx+sinxcosx)#
#=sinx/(sinx(1+cosx))#
#=1/(1+cosx)#
#=RHS#

Related questions
Impact of this question
795 views around the world
You can reuse this answer
Creative Commons License