Question

Reduce the given express (tant+cott)/(csct)

Answer 1

To reduce (tan(t) + cot(t)) / csc(t), start by expressing tan(t), cot(t), and csc(t) in terms of sine and cosine, simplify using trigonometric identities, and apply the Pythagorean identity to get the final reduced form sec(t) * csc(t).

Step-by-step explanation:

To reduce the given expression (tan(t) + cot(t)) / csc(t), we need to use trigonometric identities to simplify it. Let's start by expressing tan(t), cot(t), and csc(t) in terms of sine and cosine functions which are sin(t) / cos(t), cos(t) / sin(t), and 1 / sin(t) respectively. Then we can write:

• tan(t) as sin(t) / cos(t)
• cot(t) as cos(t) / sin(t)
• csc(t) as 1 / sin(t)

Now, let's substitute these into our expression:

(sin(t) / cos(t) + cos(t) / sin(t)) / (1 / sin(t))

This simplifies to:

(sin2(t) + cos2(t)) / (sin(t) * cos(t))

Next, we use the Pythagorean identity which states that sin2(t) + cos2(t) = 1, so the expression further reduces to:

1 / (sin(t) * cos(t))

Lastly, since sin(t) * cos(t) is the denominator, we can express the final reduced form as:

sec(t) * csc(t)