How do you solve #cot^2x/(1+cscx)=cotx(secx-tanx)#?

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Answer 1 · 2016-07-24T03:44:47

The question should say to prove, not to solve, because this equation is true to all values of x, making it an identity.

#(csc^2x - 1)/(1 + cscx)=cosx/sinx(1/cosx - sinx/cosx)#

#((cscx + 1)(cscx - 1))/(cscx + 1)=1/sinx - 1#

#((cancel(cscx + 1))(cscx- 1))/cancel(cscx + 1) = 1/sinx - 1#

#cscx - 1=(1 - sinx)/sinx#

#1/sinx - 1=(1 - sinx)/sinx#

#(1 - sinx)/sinx = (1 - sinx)/sinx#

Identity proven!!

Hopefully this helps!