Answer :

tan 2A = cot (A - 24⁰)

We know that tan θ = cot (90⁰ - θ)

cot (90⁰ - 2A) = cot (A - 24⁰)

⇒ 90⁰ - 2A = A - 24⁰
⇒ 90⁰ + 24⁰ = A + 2A
⇒ 90⁰ + 24⁰ = 3A

⇒ 114⁰ = 3A

⇒ A = 38⁰

Or

Consider (sin233⁰ + sin257⁰),

We know that sin θ = cos (90⁰ - θ)

sin233⁰ + sin257⁰ = sin233⁰ + cos2(90⁰ - 57⁰)

= sin233⁰ + cos233⁰

= 1

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