Prove the identity 1 cos 2t cot t sin 2tSolutionSolution t

Prove the identity. 1 + cos 2t = cot t sin 2t

Solution

Solution:

to prove 1+cos(2t) = cot(t) sin(2t)

Let\'s take Right hand side (RHS)

cot(t) sin(2t) = (cos(t)/ sin(t) ) (2sin(t) cos(t))

= 2cos(t) cos(t)

= 2cos²(t)

As we know that

cos 2t = 1-2(1-cos² t) = 2 cos² t - 1. ( by cosine double angle formula )

2cos²(t) = 1 + cos(2t) = Left hand side

therefore LHS = RHS

Hence proved