Question

1. Prove the identity (1+cosecx )(1-secx)=cosx cotx.​

Answer 1

Answer:

COS(x) * SEC(x)] + [COT(x) * SEC(x)]

Now, sec(x) = 1/cos(x) and cot(x) = cos(x)/sin(x), so, this comes out as

cos(x) * (1/cos(x)) = 1, and

cot(x) = [cos(x)/sin(x)] * [1/cos(x)] = 1/sin(x) = cosec(x).

Hence, [cos(x) + cot(x)]*(sec(x)) = 1 + cosec(x).