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tan^2 X=1-e^2, then find the value of sec X+(tan^3 X*cosecX)

tan^2 X=1-e^2, then find the value of sec X+(tan^3 X*cosecX)

Grade:10

1 Answers

kumaran
30 Points
4 years ago
=sec (x) + (tan^3(x) * cosec(x))
=sec (x) + (tan^2(x)*tan(x)*cosec(x)
=sec(x) + (tan^2(x)*sec(x))              {since tanx*cosecx=(sinx/cosx)(1/sinx)=secx}
=sec(x) [1 + tan^2x ]           [taking sec(x) out]
=sec^3x                [since 1 + tan^2x=sec^2x]
also tan^2x=1-e^2
=sec^2x-1 = 1-e^2
=secx=(1-e^2)^1/2
=sec^3x=[(1-e^2)^3/2] is the answer

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