Question

Prove that cos–1 ((cos θ + cos φ)/(1 + cos θ cos φ)) = 2 tan-1 (tan θ/2 tan φ/2)

Answer 1

Step-by-step explanation:

R.H.S. = 2 tan^-1 (tan θ/2 tan φ/2)

= cos^-1 [(1 - tan^2 θ/2 tan^2 φ/2) / (1 + tan^2 θ/2 tan^2 φ/2)

= cos^-1 [{1 – (sin^2 θ/2 sin^2 φ/2)/(cos^2 θ/2 cos^2 φ/2)}/ {1 + (sin^2 θ/2 sin^2 φ/2)/(cos^2 θ/2 cos^2 φ/2)}]

On simplifying this term we obtain

cos^-1 [(cos θ +  cos φ)/(1 + cos (θ - φ) – sin θ sin φ]

= cos^-1 [(cos θ + cos φ)/ (1 + cos θ cos φ)]

= L.H.S

Answer 2

Answer:

r theta sin theta m theta u theta

Step-by-step explanation:

hence noticed

sin theta by 2