Question

sin22.5 deegrre ki value​

Answer 1

Step-by-step explanation:

sinθ2=±√1−cosθ2sin⁡θ2=±1−cos⁡θ2where the sign of the right-hand side is dependent on the location of θθ. Since the angle whose sine we want to find is 22.5∘22.5∘, which is in the first quadrant, we take the positive sign of the expression. If we take θ2=22.5∘θ2=22.5∘, then we have θ=45∘θ=45∘ so we can apply the formula assin22.5∘=√1−cos45∘2=√1−√222=√2−√24sin22.5∘=√2−√22sin⁡22.5∘=1−cos⁡45∘2=1−222=2−24sin⁡22.5∘=2−22This is the exact value of the expression. It is approximately equal to 0.38270.3827.

Answer 2

Let 22.5° be equal to x

So, 2x becomes 45°

So we have to create a relation between trigonometric functions such that angle a must be related to angle b.

One of such relations which can be used here is
$\cos(2x) = 1 - 2 { \sin \: x }^{2}$

Solving for sin x gives,

$\cos(45) = 1 - 2 \sin^{2} x \\ \\ \frac{1}{ \sqrt{2} } - 1 = - 2 \sin^{2}x \\ \sin^{2}x = \frac{1 - \frac{1}{ \sqrt{2} } }{2} = \frac{2 - \sqrt{2} }{4} \\ \\ \sin(x) = \frac{ \sqrt{2 - \sqrt{2} } }{2}$



Subtitute for x as 22.5 above and tada you have the value.