Question

Simplify the trigonometric expression.


`\frac{sinx} {cscx+cotx}`

Answer 1

To simplify the expression sinx / (cscx + cotx), convert cscx and cotx to sinx and cosx, find a common denominator, and simplify to get the result sin^2(x) / (sin(x) + cos(x)).

Step-by-step explanation:

To simplify the trigonometric expression sinx / (cscx + cotx), we need to use trigonometric identities to rewrite the expression in a simpler form.

Step-by-step simplification:

1. Convert cscx and cotx to sinx and cosx using the identities csc(x)=1/sinx and cot(x) = cos(x)/sin(x).
2. Rewrite the expression using these identities: sin(x) / (1/sin(x) + cos(x)/sin(x)).
3. Find a common denominator for the terms in the denominator, which is sin(x).
4. Simplify the denominator: sin(x) / (sin(x)/sin(x) + cos(x)/sin(x)) becomes sin(x) / ((sin(x) + cos(x)) / sin(x)).
5. Multiply both numerator and denominator by sin(x): sin(x) * sin(x) / (sin(x) + cos(x)).
6. Simplify the expression by canceling out sin(x) in the numerator and denominator: sin2(x) / (sin(x) + cos(x)).

Therefore, the simplified expression is sin2(x) / (sin(x) + cos(x)).