First slide

Compound angles

Question

If $A = \sin 45^{\circ} + \cos 45^{\circ}$ and $B = \sin 44^{\circ} + \cos 44^{\circ}$ then

Moderate

A

A>B
B

A<B
C

A=B
D

none of these

Solution

$\begin{matrix} A = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} = \sqrt{2} \sin 90^{\circ} \\ B = \sqrt{2} [\frac{1}{\sqrt{2}} \sin 44^{\circ} + \frac{1}{\sqrt{2}} \cos 44^{\circ}] \\ = \sqrt{2} \sin (45^{\circ} + 44^{\circ}) \\ = \sqrt{2} \sin 89^{\circ} < \sqrt{2} \sin 90^{\circ} = \sqrt{2} \\ ∴ A > B \end{matrix}$

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