Mathematics: Write the expression in terms of sine and cosine, and then simplify so that no quotients appear in the final expression. sec beta - cos beta. a.1-cos^2beta b.sin^2beta c.cos^2beta d.1 e.sin beta tan beta

It should be x=-4 the answer to the your...

Write the expression in terms of sine and cosine,

alvaradolm6853

10.03.2022

Step-by-step explanation:

The expression given is: sec β - cos β ( i will write "beta" instead of the symbol β)

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

Substituting this into the the expression and doing some algebra manipulation, we have:

$sec(beta)-cos(beta)\\=\frac{1}{cos(beta)}-cos(beta)\\=\frac{1-cos^{2}(beta)}{cos(beta)}$

Using the identity $cos^{2}(x)+sin^{2}(x)=1\\$ (also $sin^{2}(x)=1-cos^{2}(x)$ ), we can now write:

$\frac{1-cos^{2}(beta)}{cos(beta)}\\=\frac{sin^2(beta)}{cos(beta)}\\=\frac{sin(beta)*sin(beta)}{cos(beta)}\\=\frac{sin(beta)}{cos(beta)}*sin(beta)$

We know $tan(x)=\frac{sin(x)}{cos(x)}$ , substituting this, we have:

$\frac{sin(beta)}{cos(beta)}*sin(beta)\\=tan(beta)*sin(beta)$

Answer choice E is the right answer.

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