Question

tanx-cotx=cosecx (solve)

Answer 1

Given : Tanx - Cotx = Cosecx

To Find : Value of x

Solution:

Tanx - Cotx = Cosecx

= Sinx/Cosx  - cosx/sinx  = 1/Sinx

=> (sin²x - cos²x)  = sinxcosx/sinx

=> sin²x - cos²x = cosx

=> 1 - cos²x  - cos²x = cosx

=> 2cos²x + cosx - 1 = 0

=>  2cos²x+ 2cosx - cosx - 1 = 0

=> 2cosx(cosx  + 1) - 1(cosx + 1) = 0

=> (2cos x - 1)(cosx + 1)  = 0

=> cosx = 1/2  cosx = - 1

x = 60°   or   x = 180°

but cotx not defined at 180°

Hence  x = 60°

identity can be :

Tanx+ Cotx = Cosecx.Secx

=> Sinx/Cosx  + cosx/sinx  = 1/SinxCosx

=> sin²x - cos²x = 1

=> 1 = 1

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