Prove that ?

tan^2.sin^2 +cos^2+2sin^2=sec^2

1 Answer
maganbhai P.
Mar 2, 2018

Please see explanation section.
#tan^2color(red)(x)sin^2color(red)(x)+cos^2color(red)(x)+2sin^2color(red)(x)=sec^2color(red)(x)#

Explanation:

I think the Question is:
#tan^2xsin^2x+cos^2x+2sin^2x=sec^2x#
#LHS=tan^2xsin^2x+cos^2x+2sin^2x##=tan^2xsin^2x+color(red)(cos^2x+sin^2x)+sin^2x##=tan^2xsin^2x+sin^2x+color(red)(1)#
#=sin^2xcolor(red)((tan^2x+1))+1#
#=sin^2x*color(red)(sec^2x)+1#
#=sin^2x/cos^2x+1#
#=tan^2x+1#
#=sec^2x#
#=RHS#

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