Question

Prove that (sectheta)(csctheta)(cottheta)=csc^2theta

Answer 1

csc = 1/sin
sec = 1/cos
cot = 1/tan

Answer 2

tan = sin/cos
thus
cot = cos/sin

Answer 3

using these proofs you can easily break this up and solve it using basic algebra

Answer 4

\[LHS = sec\theta csc\theta cot \theta = sec\theta csc\theta \frac{cos\theta}{sin\theta}\]\[ = sec\theta csc\theta cos\theta csc\theta = csc^2\theta = RHS\]

Answer 5

remember cot = cos/sin

\[\frac{1}{\cos(\theta)}\times \frac{1}{\sin(\theta)} \times \frac{\cos(\theta)}{\sin(\theta)}\]

this its solution is

\[\frac{1}{\sin(\theta)\times \sin(\theta)} = \frac{1}{sin^2(theta)}=csc^2(theta)\]