How do you prove #tanx/secx + cotx/cscx = sinx+cosx#?

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Answer 1 · 2015-05-02T02:45:16

# (sin x/cos x).(cos x/1) + (cos x/sin x)(sin x/1) =#
# = sin x + cos x#

Answer 2 · 2016-08-25T10:22:52

See the Proof in Explanation.

#"The L.H.S."=(tanx+cotx)/(secx+cscx)#

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

#={(sin^2x+cos^2x)/cancel((cosxsinx))}/{(sinx+cosx)/cancel((cosxsinx))}#

#=1/(cosx+sinx)#

#="the R.H.S."#