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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