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Alaina Marshall

Alaina Marshall

Answered question

2022-05-23

If a sin 2 θ + b cos 2 θ = m , a cos 2 ϕ + b sin 2 ϕ = n , a tan θ = b tan ϕ, prove that 1 n + 1 m = 1 a + 1 b

Answer & Explanation

Annabella Velez

Annabella Velez

Beginner2022-05-24Added 7 answers

a sin 2 θ + b cos 2 θ = m a tan 2 θ + b = m sec 2 θ a tan 2 θ + b = m ( 1 + tan 2 θ ) tan 2 θ = m b a m
so, using the same idea
tan 2 ϕ = n a b n
we also have that
tan 2 θ tan 2 ϕ = b 2 a 2

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