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Question

If sinθ+cosθ=m and secθ+cosecθ=n, then nm+1m-1=


A

m

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B

n

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C

2m

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D

2n

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Solution

The correct option is C

2m


Solve by substituting the values in given expression:

Put the given values sinθ+cosθ=m and secθ+cosecθ=n in the required expression, then

nm+1m-1=secθ+cosecθsinθ+cosθ+1sinθ+cosθ-1

Apply the algebraic identity a2-b2=(a+b)(a-b), then

nm+1m-1=secθ+cosecθsinθ+cosθ2-12

Now, applying the algebraic identity (a+b)2=a2+b2+2ab, we get

n+m+1m-1=secθ+cosecθsin2θ+cos2θ+2sinθcosθ-1=secθ+cosecθ1+2sinθcosθ-1=1cosθ+1sinθ2sinθcosθ=2sinθcosθcosθ+2sinθcosθsinθ=2sinθ+cosθ=2m

Hence, the correct option is (C).


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