Use the fundamental identities to simplify the expression.
cos(x)(1 + tan2(x))
To simplify the expression cos(x)(1 + tan^2(x)), we can use the fundamental trigonometric identity: tan^2(x) = sec^2(x) - 1.
Therefore, we can rewrite the expression as:
cos(x)(1 + tan^2(x))
= cos(x)(1 + sec^2(x) - 1)
= cos(x)(sec^2(x))
Now, since sec(x) = 1/cos(x), we can substitute that in:
cos(x)(1 + tan^2(x))
= cos(x)(sec^2(x))
= cos(x)((1/cos^2(x))^2)
= cos(x)(1/cos^2(x))
= 1/cos(x)
Hence, the simplified expression is 1/cos(x).