Question

1 / cosec A is equal to sec A *
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Answer 1

Answer:

Step-by-step explanation:

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

Edits are welcome