The value of tan theta in terms of cosec theta
tanx = sinx/cosc
= sinx/√(1 - sin^2 x)
= (1/cscx)/√(1 - 1/csc^2)
= 1/(cscx√(1 - 1/csc^2) )
replace x with theta
cot^2x + 1 = csc^2x
cotx = 1/tanx
1/tan^2x + 1 = csc^2x
1/tan^2x = csc^2x - 1
tan^2x = 1/(csc^2x - 1)
tanx = √(1/(csc^2x-1))
To find the value of tan theta in terms of cosec theta, we need to know the relationship between the two trigonometric functions.
First, let's define the terms:
- cosec(theta) = 1/sin(theta)
- tan(theta) = sin(theta) / cos(theta)
Now, since we are given cosec(theta), we can rewrite it as 1/sin(theta) in terms of sin(theta).
Using the relationship between sin(theta) and cosec(theta), we have:
cosec(theta) = 1/sin(theta)
To find tan(theta) in terms of cosec(theta), we can substitute this value of cosec(theta) into the expression for tan(theta):
tan(theta) = sin(theta) / cos(theta)
tan(theta) = (1/sin(theta)) / cos(theta)
Simplifying further, we can multiply the numerator and denominator by cos(theta) to eliminate the fraction:
tan(theta) = (1/sin(theta)) * (1/cos(theta))
tan(theta) = 1 / (sin(theta) * cos(theta))
So, in terms of cosec(theta), the value of tan(theta) is 1 / (sin(theta) * cos(theta)).