Question

Cosec A+ 1
---------------. = ( sec A + tan A )²
cosec A-1​

Answer 1

Answer:

Is cosec A + 1/ cosec A - 1 equal to (secA+tanA) ^2?

We need to prove that ,

(cosecA+1)\(cosecA−1)=(secA+tanA)2

L.H.S

cosec A = 1 / sin A

cosecA+1=>1/sinA+1

=> (1+sinA)/sinA−−−(i)

cosecA−1=>1/sinA−1

=> (1−sinA)/sinA−−−(ii)

Divide (i) and (ii)

[(1+sinA)/sinA]/[(1−sinA)/sinA]

(1+sinA)/(1−sinA)

Multiplying by ( 1+sin A ) in numerator and denominator

[(1+sinA)2]/(1−sin2A)

1 - sin^2 A = cos ^ 2 A = ( cos A ) ^ 2

(1+sinA)2/(cosA)2

a^m ÷ b^m = ( a ÷ b ) ^m

(1+sinA/cosA)2

1 / cos A = sec A

sin A / cos A = tan A

(secA+tanA)2

L.H.S = R.H.S