SOLUTION: proving identites-left hand side a) 1+sin x\1+cosec x = sin x b)1/1+cos x= cosec (cosec x-cot x) plz help me am not getting z solution Thx in advance

Algebra ->  Trigonometry-basics -> SOLUTION: proving identites-left hand side a) 1+sin x\1+cosec x = sin x b)1/1+cos x= cosec (cosec x-cot x) plz help me am not getting z solution Thx in advance      Log On


   

Question 1118513: proving identites-left hand side
a) 1+sin x\1+cosec x = sin x
b)1/1+cos x= cosec (cosec x-cot x)
plz help me am not getting z solution
Thx in advance
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
(1+sin x)/(1+csc x)
rewrite the denominator as (1+(1/sinx))=(sin x+1)/sin x
inverting the denominator and multiplying by the numerator
(1+sin x)*(sin x)/(sin x+1) = sin x
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1/(1+cos x) multiply top and bottom by conjugate (1-cos x)
this equals (1-cos x)/(1-cos^2 x)=(1-cos x)/sin^2 x)
This is 1/(sin^2 x)-[(cos x)/(sin^2 x)]
take out a sin x in both terms
(1/(sin x)) [(1/sin x)-(cos x/sin x)]
=csc x(csc x-cot x)