How do you prove that #(2sinx)/[secx(cos4x-sin4x)]=tan2x#?

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Answer 1 · 2018-05-28T05:32:58

As proved

I suppose the sum is

#(2 sin x) / (sec x (cos^4 x - sin ^4 x)) = tan 2x#

#=> (2 sin x cos x) / ((cos^2 x + sin-^2x)* (cos ^2x - sin^2x))#

#color(crimson)(sin 2x = 2 sin x cos x#, identity

#color(crimson)(cos^2 x + sin ^2 x -= 1#, identity

#color(crimson)(cos^2x - sin^2 x = cos 2x#, identity

#:. => (sin 2x) / (cos 2x) = tan 2x = R H S#