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

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

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

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