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Schach [20]
3 years ago
7

Write the expression in terms of sine and cosine, and then simplify so that no quotients appear in the final expression. sec bet

a - cos beta.
A.1-cos^2beta
B.sin^2beta
C.cos^2beta
D.1
E.sin beta tan beta
Mathematics
1 answer:
Ede4ka [16]3 years ago
3 0

Answer:

E

Step-by-step explanation:

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

<em>We know that sec(x)=\frac{1}{cos(x)}</em>

<em>Substituting this into the the expression and doing some algebra manipulation, we have:</em>

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

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

\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)

<em>We know tan(x)=\frac{sin(x)}{cos(x)}, substituting this, we have:</em>

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


Answer choice E is the right answer.

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