Question

if 0 < 5 < π/2, then minimum value of sin x + cosec X is
A) 0
B) -1
C) 1
D) 2

Answer 1

Answer: The answer is (D) 2.

Step-by-step explanation:  We are to find the minimum value of the following trigonometric expression

$\sin x+\csc x.$

We know that

$-1\leq \sin x\leq 1\\\\\Rightarrow 0\leq \sin^2x\leq 1.$

Therefore,

$\dfrac{1}{\sin x}\geq 1~~\textup{and}~~1\leq \sin^2x+1\leq 2.$

Now, we have

$\sin x+\csc x\\\\=\sin x+\dfrac{1}{\sin x}\\\\\\=\dfrac{\sin^2x+1}{\sin x}\\\\\\\leq\dfrac{2}{\sin x}\\\\\\\leq \dfrac{2}{1}=2.$

Thus, the correct option is (D) 2.

Answer 2

Answer:2

Step-by-step explanation: