Answer:
tan θ / sec θ = sin θ
Explanation:
We know that secant is the reciprocal of cosine. Therefore, we can write:
sec θ = 1/cos θ
Substituting this in the given expression, we get:
tan θ / sec θ = tan θ / (1/cos θ)
Multiplying by cos θ/cos θ to simplify the expression, we get:
tan θ / sec θ = (tan θ cos θ) / 1
We know that the tangent of an angle is equal to the sine of the angle divided by the cosine of the angle. Therefore:
tan θ = sin θ / cos θ
Substituting this in the expression above, we get:
tan θ / sec θ = (sin θ / cos θ) cos θ
Simplifying the expression further, we get:
tan θ / sec θ = sin θ
Therefore, the expression in terms of sine and cosine, simplified so that no quotients appear in the final expression, is:
tan θ / sec θ = sin θ