Question

Prove this equation ​

Answer 1

LHS:-

(cosecA-1)/(cosecA+1)

(1/sinA -1)/(1/sin A +1)

(1-sinA)/(1+sinA)

(1-sinA)(1+sinA)/(1+sinA)(1+sinA)

(1-sin²A)/(1+sinA)²

cos²A/(1+sinA)²

[cosA/(1+sinA)]²

proved

Answer 2

Heya!

L.H.S

(Cosec A - 1 )

------------------

(Cosec A + 1 )

Cosec A = 1/Sin A

=>

( 1 - Sin A )

-------------

( 1 + Sin A )

Now, Multiply NUMERATOR and DENOMINATOR by ( 1 + Sin A ) we have

=>

( 1 - Sin A ) × ( 1 + Sin A )

------------------------------

( 1 + Sin A ) × ( 1 + Sin A )

=>

( 1² - Sin² A )

----------------

( 1 + Sin A )²

Becoz ( a + b ) × ( a - b ) = a² - b²

And

( a + b ) × ( a + b ) = ( a + b )²

=>

( Cos² A )

------------

( 1 + Sin A )²

Becoz ( 1 - Sin² A ) = Cos² A

=>

{ ( Cos A ) /( 1 + Sin A ) }²

HENCE, PROVED.