Question

Perform the addition and use the fundamen (sinx)/(1+cosx)+(1+cosx)/(sinx)

Answer 1

The given trigonometric expression (sinx)/(1+cosx) + (1+cosx)/(sinx) simplifies to 2/(sinx) by finding a common denominator, using trigonometric identities, and combining like terms.

Step-by-step explanation:

The question involves simplifying a trigonometric expression: (sinx)/(1+cosx) + (1+cosx)/(sinx). To solve this, we need to find a common denominator and combine the terms. The common denominator here is sinx(1+cosx). So, we multiply the numerator and denominator of the first fraction by sinx and the numerator and denominator of the second fraction by 1+cosx to get:

• (sin2x)/(sinx(1+cosx)) + (1+cos2x)/(sinx(1+cosx))

Now add the numerators together:

• ((sin2x + 1 + 2cosx + cos2x))/(sinx(1+cosx))

Using the Pythagorean identity, we know that sin2x + cos2x = 1. The expression simplifies to:

• (2 + 2cosx)/(sinx(1+cosx)) = 2/(sinx)

Thus, our final simplified result is 2/sinx.