Question

If x = log⁡sin ⁡θ ; y = log cos θ then dy/dx is

Answer 1

Answer:

y = a sin θ

dy/dθ = a cos θ

x = a{cos θ + log tan(θ/2)}

dx/dθ = a {-sin θ + (1/tan(θ/2))sec2(θ/2))(1/2)}

= a {-sin θ + (1/sin θ)}

= a(1-sin2 θ )/sin θ

= a( cos2θ/sin θ)

dy/dx = (dy/dθ)/(dx/dθ) = a cos θ/ a( cos2θ/sin θ)

= tan θ

Hence option (2) is the answer.