maths題 help plx

Case 1
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( sin θ / csc θ )+ cot θ
= sin^2 θ + ( cos θ / sin θ )
= ( sin^3 θ + cos θ ) / sin θ
= [ ( 1 - cos^2 θ )( sin θ ) + cos θ ] / sin θ
= [ ( - sin θ ) cos^2 θ + cos θ + ( sin θ ) ] / sin θ .......


Case 2:
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cscθ + cotθ
= 1/sinθ + cosθ/sinθ
= ( 1 + cosθ )/sinθ

sinθ/ [ ( cscθ + cotθ ) / sinθ ]
= sin^2 θ / ( 1 + cosθ )
= ( 1 - cos^2 θ ) / ( 1 + cosθ )
= ( 1 + cosθ )( 1 - cosθ ) / ( 1 + cosθ )
= 1 - cosθ


Both cases cannot reach your R.H.S answer.
Hence, it is not an identity.

Please check your question if there is any typing mistake or if it only askes you to check whether it is an identity.

Hope I can help you.

sinθ / (cscθ + cotθ )= 1 + sinθ or( sinθ / cscθ )+ cotθ = 1 + sinθ?