How do you verify the identity #4 csc 2x = 2 csc^2x tan x#?

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Answer 1 · 2015-04-28T11:50:36

We will be using a Trigonometric identity to prove this-
#color(blue)(sin(2x) = 2sinxcosx#

The left hand side is # 4csc2x#

# = 4/(sin2x)# (Because #cscx = 1/sinx#)

# = 4/(2sinxcosx)#

# = color(green)(2/(sinxcosx)#

The right hand side is #2 csc^2x tan x#

# = 2*(1/sin^2x)*(sinx/cosx)# (Because #tanx = sinx/cosx#)

# = color(green)(2/(sinxcosx)#

Hence proved.