Question

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

Answer 1

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!