Question

1/sin square theta=2cosec theta.
is it possible??
give valid reason
if ur answer is no then tell how can v get 2 cosec theta
question is:
prove tanA/secA-1 +tanA/secA+1 =2cosecA

Answer 1

this is the answer use this photo

Answer 2

Hi ,

1 ) it is possible ,

here I used A instead of theta .

1/ sin²A = 2 Cosec A

1/2 = Cosec A sin² A

1/2 = ( Cosec A sin A ) sin A

1/2 = sinA [ since Cosec A sinA = 1 ]

sinA = 1/2

sinA = sin 60°

A = 60°

if A = 60°

then

1/ sin² A = 2 Cosec A

2 ) LHS

= tanA / ( secA+1) + tanA/(secA - 1 )

= tanA [ 1/(secA +1 ) + 1/(secA- 1 )]

= tanA [ ( secA-1 +secA-1)/(sec² A - 1² ) ]

{ since sec²A - 1 = tan² A }

=( tan A × 2sec A )/ tan² A

= 2secA / tanA

= (2 × 1/cosA)/( sinA / cosA)

= 2/sinA

= 2 cosecA

= RHS

I hope this helps you .