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KCET 2025 Math Paper

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Question : 49 of 60

Marks: +1, -0

The minimum value of

1-\sin x

is

$0$
$-1$
$1$
$2$

Solution:

To find the minimum value of the expression

f(x)=1-\sin x

, we start by considering the range of the sine function. Since

-1 \leq \sin x \leq 1

, this means the minimum value of

\sin x

is -1 .

Now, compute

f(x)

when

\sin x = -1

:

f(x)=1-(-1)=1+1=2

Check if

\sin x = 1

:

f(x)=1-1=0

Thus, the minimum value of

f(x)=1-\sin x

occurs when

\sin x = 1

, making the minimum value:

f_{\min}=0

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