Question

solve the following equation k= 1+sinx/n​

Answer 1

The solution for the given equation is x=arc sin(kn−1)

Given:

The equation is  k= 1+sinx/n​

To Find:

The value of the given equation   k= 1+sinx/n​

Solution:

$\frac{1+sinx}{n} = k$

$\frac{1+sin(x)}{n}$ = k

Multiplying n on both sides,

$\frac{1+sin(x)}{n}$n = kn

Simplify left hand side,

sin(x)+1 = kn

sinx = kn-1

Take the inverse sine of both sides of the equation to extract

from inside the sine

We get x = arcsin(kn-1)

The solution for the given equation is x=arc sin(kn−1)

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Answer 2

The solution to the following question is x= n.(arcsin(k-1)- 2πm)

Given:

K= 1+sin(x/n)

To find:

solution of k = 1+sin(x/n)

Solution:

K= 1+sin(x/n)

first, we put the 1 on the left-hand side. i.e., we subtract 1

Therefore,

k-1 = sin(x/n)

we take arc on both sides of the equation

arcsin(k-1) = arcsin(sin(x/n))

arcsin(k-1)=x/n + 2πm

we take 2πm to the left-hand side.

Therefore,

arcsin(k-1)- 2πm=x/n

then we put the n on the left-hand side. i.e., multiply by n

we get,

x= n.(arcsin(k-1)- 2πm)

The solution of K= 1+sin(x/n) is x= n.(arcsin(k-1)- 2πm)

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