Question

Write the following in terms of sin Θ and cos Θ; then simplify if possible. (Leave your answer in terms of sin Θ and/or cos Θ.)

sec Θ − tan sin Θ

Answer 1

cos Θ

Explanation:

I assume you mean

sec Θ − tan Θ sin Θ =

= 1 / cos Θ - sin Θ / cos Θ × sin Θ

= 1 / cos Θ - sin² Θ / cos Θ

= (1 - sin² Θ) / cos Θ Eq. 1

Recall the identity: sin² Θ + cos² Θ = 1

Subtract sin² Θ from both sides:

cos² Θ = 1 - sin² Θ

Substitute 1 - sin² Θ with cos² Θ in Eq. 1

= cos² Θ / cos Θ

= cos Θ