KVPY SX SB Exam 2015 Question Paper

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Question : 7 of 120

Marks: +1, -0

The number of real numbers

λ

for which the equality

{\sin(λα)}/{\sinα}-{\cos(λα)}/{\cosα} = λ - 1

,
holds for all real α which are not integral multiples of

π/2

is -

1
2
3
Infinite

Solution:

{\sin(λα)}/{\sinα}-{\cos(λα)}/{\cosα} = λ - 1

By observation

\sin(λα) \cosα - \cos (λα) \sinα

= (λ- 1) \sinα \cosα

\sin(λ - 1)α = (λ - 1) \sinα\cosα

clearly

λ= 1,λ = 3

is solution

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