Question

Prove this identity sinx+ sin2x/1 + coax+ cos2x= tanx​

Answer 1

To prove the given identity, we can simplify the left side by using double-angle identities and combining like terms. We can then rewrite the expression using the identity tan(x) = sin(x)/cos(x).

Step-by-step explanation:

To prove the given identity: sinx+ sin2x/1 + coax+ cos2x= tanx

Let's start by simplifying the left side of the equation:

sin(x) + (sin(2x))/(1 + cos(x) + cos(2x))

Next, we can use the double-angle identities for sine and cosine:

sin(x) + 2sin(x)cos(x)/(1 + cos(x) + 2cos^2(x) - 1)

Now, we can combine like terms:

sin(x) + 2sin(x)cos(x)/(cos(x) + 2cos^2(x))

Finally, we can use the identity tan(x) = sin(x)/cos(x) to rewrite the expression:

tan(x)