d/(dx)((1-sin 2x)/(1+sin 2x)) is equal to A) sec^2 x B) -sec^2 (pi/4 -x) C) sec^2 (pi/4 +x) D) sec^2 (pi/4 -x)

Destiney Barrett

Destiney Barrett

Answered question

2023-01-15

ddx1-sin2x1+sin2xis equal to
A)sec2x
B)-sec2π4x
C)sec2π4+x
D)sec2π4x

Answer & Explanation

Gremoli9bs

Gremoli9bs

Beginner2023-01-16Added 10 answers

The right option is B -sec2π4x
Solution for the right option:
Step 1. Find the differentiation of the given expression:
We know, y=1-sin2x1+sin2x
y=cos2x+sin2x-2sinxcosxcos2x+sin2x+2sinxcosx sin2θ+cos2θ=1,sin2θ=2sinθcosθ
y=(cosxsinx)2(cosx+sinx)2
y=(cosxsinx)(cosx+sinx)
Step 2. Divide numerator and denominator by cosx
y=(1-tanx)(1+tanx)
y=(tanπ4-tanx)(tanπ4+tanx) tan(π4)=1
y=tanπ4-x tan(θ-ϕ)=tanθ-tanϕtanθ+tanϕ
Differentiate it with respect to x, we get
dydx=-sec2(π4x)
Thus, option (B) is right.

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