a) tan^2 x + cot^2 x
b) cos^2 x + sin^2 x
c) sec^2 x + cos^2 x
d) sec^2 x + csc^2 x
please help 🙁
3 Answers
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d
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tan x +cot x = (sin x / cos x)+ (cos x /sin x)
=(sin^2x +cos^2 x) / sinx cos x = 1 /(sin x cos x) ..(.i)
L>H>S=(tanx+cotx)^2
= 1/ (sin^2x cos^2x) [ from(i)]
=(sin^2x +cos^2x) / (sin^2x cos^2x)
= { sin^2x/(sin^2x cos^2x)} + {cos^2x/(sin^2x cos^2x)}
={ 1/ cos^2x } + { 1/ sin^2x}
= sec^2 x + cosec ^2x
ans. is (d)
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(tanx + cotx)2= (sinx/cosx + cosx/sinx)^2
=(sin^2x+cos^2x)^2/ sin^2xcos^2x=1 /sin^2xcos^2x
= (sin^2x+cos^2x)/sin^2xcos^2x= sec^2x +cosec^2x
d is the right answer
