cot square divided by 1 minus tan A + sin cube A divided by Sin A minus Cos A is equals to 1 + sin a cos A
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From LHS -
{ Cos ²∅ / 1 - sin∅/ cos∅ } + { sin ³∅ / sin∅ - cos ∅ }
⇒ { Cos² ∅ × cos∅/ cos∅- sin ∅ } + { sin ³∅/ sin ∅ - cos∅ }
⇒. { cos³∅ / - ( sin ∅ - cos∅ ) } + { sin³∅ / sin ∅ - cos∅ }
⇒. cos³∅ - sin³∅ / sin ∅ - cos∅
{ Using the Formula = a³ - b³ ( a - b ) ( a² + b² + ab }
hence we get ,
⇒ { ( sin∅ - cos∅ ) ( sin ²∅ + cos² ∅+ sin∅. × cos∅ )} / sin∅ - cos ∅
We all know that,
sin²∅ + cos²∅ = 1
Then we finally get ,
➯ 1 + sin ∅. Cos∅
Hence it is proved
Step-by-step explanation:
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