Cosec A-1/cosec A+1 =(cos A)/1 + sin a

1
by alexbenny24

2015-05-11T21:11:34+05:30
TO PROVE ;-

⇒ Cosec  A - 1 / cosec  A + 1  = ( cos  A ) / 1  + sin a

PROOF ;-

⇒ ''Here we need to prove that L. H . S is equal to R. H. S''

⇒ Now, first let us go with Left hand side-

With the help of the given identity we need to prove it -

↓
Cosec A + Cot A - { Cosec A + Cot A} { Cosec A - Cot A } / Cot A - Cosec  A + 1

⇒ Left Hand Side

Cosec A + Cot A { 1 - cosec A + cot A }  /  cot A - cosec A + 1

⇒ Cosec A + Cot A                    { { 1 - cosec A + cot A }  /  cot A - cosec A +                                                      1 because it gets cancelled }
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⇒ Right hand side

⇒ 1 +cos A / Sin A                         [ given }

⇒ 1 sin A  cos A / sin A

⇒cosec A + cot A

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Hence R.H.S and L.H.S are same. so hence proved

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