Answer:
From given relation the value of β is 37.5°
Step-by-step explanation:
Given as :
α and β are two acute angles of right triangle
Acute angle have measure less than 90°
Now given as :
= ![cos(2x +\frac{3x}{2})](https://tex.z-dn.net/?f=cos%282x%20%2B%5Cfrac%7B3x%7D%7B2%7D%29)
Or,
= ![cos(2x +\frac{3x}{2})](https://tex.z-dn.net/?f=cos%282x%20%2B%5Cfrac%7B3x%7D%7B2%7D%29)
SO,
= ![2x+\frac{3x}{2}](https://tex.z-dn.net/?f=2x%2B%5Cfrac%7B3x%7D%7B2%7D)
Or, 90° =
+ ![\frac{x}{2}+2x](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D%2B2x)
or, 90° =
+ 4x
Or, 90° = ![\frac{12x}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B12x%7D%7B2%7D)
So, x =
= 15°
∴
= ![sin(\frac{15}{2} + 30)](https://tex.z-dn.net/?f=sin%28%5Cfrac%7B15%7D%7B2%7D%20%2B%2030%29)
So,
= sin
∴ The value of Ф_1 =
= 37.5°
Similarly
= ![cos(30 +\frac{45}{2})](https://tex.z-dn.net/?f=cos%2830%20%2B%5Cfrac%7B45%7D%7B2%7D%29)
So ,The value of Ф_2 =
= 52.5°
∵ β
α
So, As 37.5°
52.5°
∴ β = 37.5°
Hence From given relation the value of β is 37.5° Answer
It is an acute triangle since all the sides are less than 90 degrees (it's also equilateral)
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