Answer :
sin 2θ + sin 2ϕ = 1/2
⇒ 2sin (θ + ϕ) cos (θ – ϕ) = 1/2 …(I)
cos 2θ + cos 2ϕ = 3/2
⇒ 2cos (θ + ϕ) cos (θ – ϕ) = 3/2 …(II)
Dividing equation (I) by equation (II) –
tan (θ + ϕ) = 1/3
⇒ tan2 (θ +ϕ) = 1/9
⇒ 1 + tan2 (θ + ϕ) = 1 + 1/9 = 10/9
Substituting this value of cos (θ + ϕ) in (II), we get –
(Ans)
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