Question

Simplify the left side of equation so it looks like the right side. cos(x) + sin(x) tan(x) = sec (x)

Answer 1

Step-by-step explanation:

Consider LHS

$\cos(x) + \sin(x) \tan(x) = \sec(x)$

Apply quotient identies

$\cos(x) + \sin(x) \times \frac{ \sin(x) }{ \cos(x) } = \sec(x)$

Multiply the fraction and sine.

$\cos(x) + \frac{ \sin {}^{2} (x) }{ \cos(x) } = \sec(x)$

Make cos x a fraction with cos x as it denominator.

$\cos(x) \times \cos(x) = \cos {}^{2} (x)$

so

$\frac{ \cos {}^{2} (x) }{ \cos(x) } + \frac{ \sin {}^{2} (x) }{ \cos(x) } = \sec(x)$

Pythagorean Identity tells us sin squared and cos squared equals 1 so

$\frac{1}{ \cos(x) } = \sec(x)$

Apply reciprocal identity.

$\sec(x) = \sec(x)$