Question

cos squared theta by 1 minus 10 theta + sin cube theta by sin theta minus cos theta is equal to 1 + sin theta + cos theta prove it​

Answer 1

Step-by-step explanation:

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 Formula - a³ - b³ ( a - b ) ( a² + b² + ab }

Now ,

⇒ { ( sin∅ - cos∅ ) ( sin ²∅ + cos² ∅+ sin∅. × cos∅ )} / sin∅ - cos ∅

We know sin²∅ + cos²∅ = 1

Then ,

➯ 1 + sin ∅. Cos∅

Hence proved