Question

Prove that:
cosec A (1 + cos A) (cosec A- cot A) = 1
​

Answer 1

Step-by-step explanation:

cosec A ( 1+cos A)(cosec A-cotA)=1

1÷sinA(1+cosA)(1÷sinA - cosA÷sinA)=1

1÷ sinA(1+cosA)( 1-cosA÷ sinA)=1

1÷sinA(1-cos^2A÷sinA)=1

1÷sinA(sin^2A÷sinA)=1

1÷sinA×sinA=1

1=1

L.H.S = R.H.S