Ji cos38' sec(90-2x)ji equal to 1 ,then angle 'x' is
To solve the equation, ji cos38' sec(90-2x)ji = 1, for the angle 'x', we will follow these steps:
Step 1: Simplify the equation
Using some trigonometric identities, we can simplify the given equation.
cos38' sec(90-2x) = 1
Now, let's evaluate sec(90-2x). We know that:
sec(90 - θ) = cscθ
Therefore:
sec(90-2x) = csc(2x)
Now, the equation becomes:
cos38' csc(2x) = 1
Step 2: Substitute and simplify
We will substitute the values of cos38' and csc(2x) into the equation.
Recall that:
cos(90 - θ) = sinθ
cos38' = sin(90 - 38') = sin52'
Therefore, the equation becomes:
sin52' csc(2x) = 1
Step 3: Use the reciprocal identity
The reciprocal identity states that:
cscθ = 1/sinθ
Now, the equation becomes:
sin52' * (1/sin(2x)) = 1
We can simplify as follows:
sin52' / sin(2x) = 1
Step 4: Apply the quotient identity
The quotient identity states that:
sinθ / sinφ = 1 / (cosecθ cscφ)
Using this identity, we can rewrite the equation:
1 / (cosec(2x)) = 1 / (sin52')
Equating the denominators, we get:
cosec(2x) = sin52'
Step 5: Evaluate the angle x
Now, we can solve for 'x' by evaluating the angle for which cosec(2x) is equal to sin52'.
cosecθ = 1/sinθ, so
cosec(2x) = 1/sin(2x)
To find 'x', we need to find the angle for which sin(2x) = 1/sin52':
sin(2x) = 1/sin52'
Taking the inverse sine of both sides, we get:
2x = arcsin(1/sin52')
Finally, solve for 'x' by dividing by 2:
x = (arcsin(1/sin52')) / 2
Please note that the values used in this explanation are in degrees. Make sure to use the appropriate units (degrees or radians) when performing calculations.