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1.Relation and Function
medium
જો $x \in R$ માટે $f(x) = \frac{{{{\cos }^2}x + {{\sin }^4}x}}{{{{\sin }^2}x + {{\cos }^4}x}}$ , તો $f(2002) = $
A
$1$
B
$2$
C
$3$
D
$4$
Solution
(a) $f(x) = \frac{{{{\cos }^2}x + {{\sin }^4}x}}{{{{\sin }^2}x + {{\cos }^4}x}}$
==> $f(x) = \frac{{{{\cos }^2}x + {{\sin }^2}x(1 – {{\cos }^2}x)}}{{{{\sin }^2}x + {{\cos }^2}x(1 – {{\sin }^2}x)}}$
==> $f(x) = \frac{{{{\sin }^2}x + {{\cos }^2}x – {{\sin }^2}x{{\cos }^2}x}}{{{{\sin }^2}x + {{\cos }^2}x – {{\sin }^2}x{{\cos }^2}x}}$
==> $f(x) = 1$ ==> $f(2002) = 1$.
Standard 12
Mathematics
