Question # C
+
2 x + sec? x, then
k? +1
(d) k
If f(x) = cos x + Sep 2
(a) f(x) <1
15. Which of the
f(x) <1
(b) f(x)=1
h of the following is incorrect?
(c) 2

# C
+
2 x + sec? x, then
k? +1
(d) k
If f(x) = cos x + Sep 2
(a) f(x) <1
15. Which of the
f(x) <1
(b) f(x)=1
h of the following is incorrect?
(c) 2

Solution ( f(x)=cos ^{2} x+sec ^{2} x )
( cos ^{2} x=1-sin ^{2} x )
( sec ^{2} x=1+tan ^{2} x )
( f(x)=1-sin ^{2} x+tan ^{2} x+1 )
( Rightarrow 2+frac{sin ^{2} x}{cos ^{2} x}-sin ^{2} x )
( Rightarrow 2+frac{sin ^{2} x-sin ^{2} x cos ^{2} x}{cos ^{2} x} )
( Rightarrow 2+frac{sin ^{2} xleft(1-cos ^{2} xright)}{cos ^{2} x} )
( Rightarrow 2+frac{sin ^{4} x}{cos ^{2} x} )
Here ( frac{sin ^{4} x}{cos ^{2} x} geq 0 )
( therefore f(x) geq 2 )
Hence (D) is the correct answer.

Solution