Question

Simplify sin x / sec x +1

Answer 1

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

Explanation:

To simplify sin(x)/(sec(x)+1), we can first convert the secant function to its equivalent form in terms of cosine:

sec(x) = 1/cos(x)

Substituting this in the expression, we get:

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

We can simplify the denominator by finding a common denominator:

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

Next, we can simplify the expression by multiplying the numerator and denominator by the reciprocal of the complex fraction in the denominator:

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

Simplifying this, we get:

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

Therefore, sin(x)/(sec(x)+1) simplifies to sin(x)cos(x) / (1+cos(x)).