Question

If f(x)=sin^4x+cos²x/sin²x+cos^4x, then f(2002) is:
OPTIONS ARE:
a)0
b)2
c)3
d)1
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Answer 1

Answer:

f(x)

={Sin^4(x)+cos^2(x)}/{sin^2(x)+cos^4(x)}

=[{Sin^2(x)}^2+cos^2(x)]/{sin^2(x)+cos^4(x)}

=[{1-cos^2(x)}^2+cos^2(x)]/{sin^2(x)+cos^4(x)}

={1–2.cos^2(x)+cos^4(x)+cos^2(x)}/{sin^2(x)+cos^4(x)}

={1-cos^2(x)+cos^4(x)}/{sin^2(x)+cos^4(x)}

={Sin^2(x)+cos^4(x)}/{sin^2(x)+cos^4(x)}

=1

So

f(x)=1,(for any value of x)

f(x) is constant function.

f(2002)=1.