Question

Verify the identity (sinx+tanx)/(cosx+1)=tanx

Answer 1

To verify the identity (sinx+tanx)/(cosx+1)=tanx, we need to manipulate the expression on the left side until it is equal to tanx.

Step-by-step explanation:

To verify the identity (sinx+tanx)/(cosx+1)=tanx, we need to manipulate the expression on the left side until it is equal to tanx.

1. Start by multiplying both the numerator and denominator of the left side by cosx. This gives us (sinx/tanx + 1)/(cosx + cosx).
2. Next, simplify the expression in the numerator. The term sinx/tanx can be rewritten as sinx/cosx = tanx.
3. Now, substitute tanx into the numerator, giving us (tanx + 1)/(cosx + cosx).
4. Finally, simplify the denominator by combining like terms. (cosx + cosx) = 2cosx.

Therefore, the left side of the equation simplifies to (tanx + 1)/(2cosx), which is equal to tanx as desired.