Rewrite 2sinx/(cotx+cscx) as an expression that doesn't involve a fraction.

To rewrite the expression 2sinx/(cotx+cscx) without involving a fraction, we can use the concept of reciprocal identities. The reciprocal of a trigonometric function is equal to the reciprocal of its numerator divided by the reciprocal of its denominator.

Let's start by finding the reciprocal of cotx and cscx:
Reciprocal of cotx = 1/tanx
Reciprocal of cscx = 1/sinx

Now, let's substitute these reciprocal identities into the given expression:
2sinx/(cotx+cscx)
= 2sinx/(1/tanx + 1/sinx)

To add fractions, we need a common denominator. The least common denominator (LCD) of tanx and sinx is sinx * tanx. So, we can rewrite the expression as:
= 2sinx/(sinx*tanx/sinx + 1/sinx)
= 2sinx/(tanx + 1/sinx)

To avoid the fraction, we can multiply the numerator and denominator by sinx to get rid of it in the denominator:
= 2sinx * sinx /[(tanx * sinx) + (1/sinx * sinx)]
= 2sin^2x / (tanx * sinx + 1)

Therefore, the expression 2sinx/(cotx+cscx) rewritten without involving a fraction is 2sin^2x / (tanx * sinx + 1).