Given :
An equation, 2cos ß sin ß = cos ß .
To Find :
The value for above equation in (0, 2π ] .
Solution :
Now, 2cos ß sin ß = cos ß
2 sin ß = 1
sin ß = 1/2
We know, sin ß = sin (π/6) or sin ß = sin (5π/6) in ( 0, 2π ] .
Therefore,
Hence, this is the required solution.
The three numbers will be 12, 7, 2 and 3, 7, 11.
<h3>What is a sequence?</h3>A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.
Let the three consecutive numbers be a, a + d, and a + 2d
The sum of three numbers which are consecutive terms of an A.P. is 21.
a + a + d + a + 2d = 21
3(a + d) = 21
a = 7 - d
If the second number is reduced by 1 and the third term is increased by 1 we obtain the geometric product.
Then the number will be a, a + d − 1, a + 2d + 1. Then we have
On simplifying, we have
36 = a (8 + d)
a² - 15a + 36 = 0
On factorizing, the value of a will be
a² - 15a + 36 = 0
a² - 12a - 3a + 36 = 0
(a - 12)(a - 3) = 0
a = 3, 12
If a = 12, then the value of d will be
d = 7 - 12
d = -5
If a = 3, then the value of d will be
d = 7 - 3
d = 4
Then the three numbers will be 12, 7, 2 and 3, 7, 11.
More about the sequence link is given below.
#SPJ1
The given angles are 95° and 135, and the value of x is 40.
<h3>What is the angle sum property?</h3>The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
The given angles are 95° and 135.
Let's consider the adjacent angle of 135 to be z.
So, as we can see that both angles make a linear pair.
z + 135 = 180
z = 180 - 135
z = 45
Let's consider the interior angle to be y.
then,
y = 95 ( vertically opposite angle)
Now, The angle sum property
x + y + z = 180
x = 180 - 95 + 45
x = 40
Thus, the value of x is 40.
Learn more about the triangles;
#SPJ1
