Question

Verify the identity. Justify each step.

tanQ + cotQ = 1/sinQ cosQ

I understand that tanQ = sinQ/cosQ

cotQ = 1/tanQ

cotQ = cosQ/sinQ

I'm just having a brain fart!!.. Lol

Answer 1

LHS = tan Q + cot Q
= sin Q/cos Q + cos Q/sin Q
= sin² Q + cos²Q/cos Q. sin Q
= 1/sin Q. cos Q
= RHS
LHS = RHS

here, we used the identity :
tan A = sin A/cos A
cot A = cos A/sin A
sin²A+cos²A = 1

hope it helps