NIMCET 2013 Question Paper with solutions

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Question : 33 of 120

Marks: +1, -0

If sin x + a cos x = b. then what is the expression for | a sin x - cos x| in terms of a and b ?

$√{a^2-b^2-1}$
$√{a^2+b^2-1}$
$√{a^2+b^2+1}$
$√{a^2-b^2+1}$

Solution:

Given

\sin x+a\cos x=b

..(i)
Let

a\sin x-\cos x=p

...(ii)
Squaring and adding Eqs (i) and (li), we get

\sin^{2}x+a^{2}\cos^{2}x+a^{2}\sin^{2}x+\cos^{2}x=b^{2}+p^{2}

⇒p^2=1+a^2-b^2

Hence ,

|p|={|a\sin x-\cos x|}√{1+a^2-b^2}

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