The expression 1+cos2x/sin2x is equivalent to ?

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Answer 1 · 2018-05-11T04:51:34

#=1+1/2cotx+1/2tanx#

Recall the identities

#cos2x=cos^2x-sin^2x#

#sin2x=2sinxcosx#

Applying these to the given expression, we get

#1+(cos^2x-sin^2x)/(2sinxcosx)=1+(cos^cancel(2)x)/(2sinxcancel(cosx))-sin^cancel(2)x/(2cancel(sinx)cosx)#

#=1+cosx/(2sinx)-sinx/(2cosx)#

Recalling that #cosx/sinx=cotx, sinx/cosx=tanx,# we get

#=1+1/2cotx+1/2tanx#