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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Given that $\cos 6x=a\cos^6x+b\cos^4x+c\cos^2x+d$ for any real number $x$, find the value of $a+b+c$.
Solution
Given: $\cos 6x=a\cos^6x+b\cos^4x+c\cos^2x+d$ Put $x=0$$\cos 0=a\cos^6 0+b\cos^4 0+c\cos^2 0+d$
$1=a+b+c+d$ ...(1)
Put $x=\frac{\pi}{2}$
$\cos 3\pi=a\cos^6\frac{\pi}{2}+b\cos^4\frac{\pi}{2}+c\cos^2\frac{\pi}{2}+d$
$-1=d$ ...(2)
From (1),
$a+b+c+d=1$
$a+b+c-1=1$
$a+b+c=2$
Answer: $2$
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