Sinx/1+cosx = 1/sinx - 1/tanx prove the above?

Please help and thank you

2 Answers
Ratnaker Mehta
May 26, 2018

Please see a Proof in Explanation.

Explanation:

#sinx/(1+cosx)#,

#=sinx/(1+cosx)xx(1-cosx)/(1-cosx)#,

#={sinx(1-cosx)}/(1-cos^2x)#,

#={sinx(1-cosx)}/sin^2x#,

#=(1-cosx)/sinx#,

#=1/sinx-cosx/sinx#,

#=1/sinx-cotx#,

#=1/sinx-1/tanx#, as desired!

Sonnhard
May 26, 2018

Use #sin^2(x)=1-cos^2(x)#

Explanation:

From
#sin^2(x)=1-cos^2(x)#
we get
#sin(x)/(1+cos(x))=(1-cos(x))/sin(x)#
and this is
#sin(x)/(1+cos(x))=1/sin(x)-cos(x)/sin(x)#
and we get
#sin(x)/(1+cos(x))=1/sin(x)-1/tan(x)#

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