How do you verify #(2 + cos^2 x)(1+ tan^2 x)= 3 + 2tan^2 x#?

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Answer 1 · 2016-10-07T20:10:43

see below

#(2+cos^2x)(1+tan^2x)=3+2 tan^2x#

Left Side :#=(2+cos^2x)(1+tan^2x)#

#=2+2tan^2x+cos^2x+cos^2xtan^2x#

#=2+2tan^2x+cos^2x+cos^2x sin^2x/cos^2x#

#=2+2tan^2x+cos^2x+cancel(cos^2x) sin^2x/cancel(cos^2x)#

#=2+2tan^2x+cos^2x+sin^2x#

#=2+2tan^2x+1#

#=3+2tan^2x#

#:.=#Right Side