Question

Simplify 6sin θsec θ.

Choices
A) 6 tan θ
B) 6 cos θ
C) 6 cot θ
D) 6

Answer 1

A.

Explanation:

sec(x)=1/cos(x)

So you have 6sin(x)*1/cos(x) which gives you 6*sin(x)/cos(x)

Since sin(x)/cos(x)=tan(x)

then you can rewrite this as 6tan(x)

Answer 2

A) 6 tan θ

Explanation:

Given Expression:

6 sin θ sec θ

= 6 sin θ (1/cosθ)

= 6 sin θ/cos θ

= 6 tan θ

In the second step, we substituted 1/cos in place of sec because cos and sec are reciprocals of each other.

In the last step, we know used the formula:

sinθ/cosθ = tanθ