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Simplify the expression. sin^2 Ø/ csc Øtan^2 Ø

Simplify the expression. sin^2 Ø/ csc Øtan^2 Ø-example-1

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Answer: OPTION (B): sin θ cos^2 θ

Therefore, The simplified expression is OPTION (B): sin θ cos^2 θ,

Which corresponds to:

sin^2 θ / csc θtan^2 θ is OPTION (B): sin θ cos^2 θ,

  • Explanation:

Rewrite In Terms of SINE and COSINE:

sin^2 θ / 1 / sinθ * sin^2 θ / cos^2 θ

  • Simplify the Denominator:

sin^2 θ / sin^3 θ / cos^2 θ

  • Multiply by the Reciprocal:

sin^2 θ * cos^2 θ / sin^3 θ

  • Cancel out the Common Factors:

sin^2 θ * cos^2 θ / sin^3 θ = sin θ * cos^2 θ / sin^2 θ

  • Cancel sin θ from Numerator and Denominator:

sin θ * cos^2 θ / sin^2 θ = sin θ cos^2 θ

  • Draw the Conclusion: Match with the given options:

Therefore, Therefore, The simplified expression is

OPTION (B): sin θ cos^2 θ,

  • Which corresponds to:

sin^2 θ / csc θtan^2 θ is OPTION (B): sin θ cos^2 θ,

I hope this helps you!

User Mandeep Singh Gill
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