Which of the following is true for -0- and -

From graph of y=sin x : Let A≡(α,sinα) and B≡(β,sinβ) nbsp; respective points on curve. Let the mid point of AB be N ∴ N≡(α+β2,sinα+sinβ2) and point M≡(α+β2, ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Position of a Point with Respect to Circle

Which of the ...

Question

Which of the following is true for $α, β \in (0, π)$ and $α \neq β$

sin (\frac{α + β}{2}) \geq \frac{sin α + sin β}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

sin (\frac{α + β}{2}) > \frac{sin α + sin β}{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

sin (\frac{α + β}{2}) < \frac{sin α + sin β}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

sin (\frac{α + β}{2}) \leq \frac{sin α + sin β}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $sin (\frac{α + β}{2}) > \frac{sin α + sin β}{2}$
From graph of $y = sin x :$

Let $A \equiv (α, sin α)$ and $B \equiv (β, sin β)$ respective points on curve.
Let the mid point of $A B$ be $N$
$∴ N \equiv (\frac{α + β}{2}, \frac{sin α + sin β}{2})$
and point $M \equiv (\frac{α + β}{2}, sin (\frac{α + β}{2}))$
As graph of $f (x)$ is downward concave, point $M$ lies above $N$
$\Rightarrow sin (\frac{α + β}{2}) > \frac{sin α + sin β}{2}$

Suggest Corrections

Similar questions

Q. Let

α = π / 5

and

A = [\begin{matrix} cos α & sin α - sin α & cos α \end{matrix}] and B = A + A^{2} + A^{3} + A^{4}

, then which of the following is/are true for

B

Q. If

a = A_{π / 2} (α, β, γ)

b = A_{π / 3} (α, β, γ)

. Which of the following is true?

Q. Which of the following is true for

α, β \in (0, \infty)

and

α \neq β

Q. For

0 < α < β,

which of the following is true

Q. Which of the following statements is incorrect for the function

g (α)

for

α \in R

such that

g (α) = \frac{π}{3} \int \frac{π}{6} \frac{{sin}^{α} x}{{cos}^{α} x + {sin}^{α} x} d x

Join BYJU'S Learning Program

Which of the following is true for α,β∈(0,π) and α≠β

Which of the following is true for $α, β \in (0, π)$ and $α \neq β$