Inverse Trigonometric Functions – cosec⁻¹(cosecx)
Graph y = cosec⁻¹(cosecx):
y = cosec⁻¹(cosecx)
cosecy = cosecx
The general solution of cosecx = cosecα is nπ + α, n ϵ z
Now general solution of cosecy = cosecx is y = nπ + x, n ϵ z
y = nπ + x ….(1)
Equation (1) Put n = 0
y = (0)π + x
y = x
Draw the graph y = cosec⁻¹(cosecx)
Example: Evaluate the cosec⁻¹(cosec2π/3)
Solution:
cosec⁻¹(cosec2π/3)
cosec⁻¹(cosec(π -π/3))
cosec⁻¹(cosec(π/3)) = π/3