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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