Question

sin2 (45 degree/2) find the value of it

Answer 1

sin 2 (45/2)=sin45°=1/√2

Answer 2

$sin^{2}\dfrac{45}{2}^{\circ}=\dfrac{\sqrt{2}-1}{2\sqrt{2}}$

Tips:

Before we solve this problem, we must know the following trigonometric formula,

$cos\theta=1-2\:sin^{2}\dfrac{\theta}{2}$

Step-by-step explanation:

Now, $sin^{2}\dfrac{45}{2}^{\circ}$

$=\dfrac{1}{2}(1-cos45^{\circ})$

• since $cos\theta=1-2\:sin^{2}\dfrac{\theta}{2}$

$=\dfrac{1}{2}(1-\dfrac{1}{\sqrt{2}})$

• since $cos45^{\circ}=\dfrac{1}{\sqrt{2}}$

$=\dfrac{1}{2}(\dfrac{\sqrt{2}-1}{\sqrt{2}})$

$=\dfrac{\sqrt{2}-1}{2\sqrt{2}}$

#SPJ3