Question

Simplify sec(t) csc(t) to a single trig function with no fractions.

a) tan(t)
b) cot(t)
c) sin(t)
d) cos(t)

Answer 1

The expression sec(t) csc(t) simplifies to cot(t), which is the cotangent of t.

Step-by-step explanation:

The question is asking to simplify the expression sec(t) csc(t) into a single trigonometric function without any fractions. Recall that sec(t) is the reciprocal of cos(t), and csc(t) is the reciprocal of sin(t). Therefore, when we multiply these two reciprocals together, the original trig functions sin(t) and cos(t) are in the denominator:

sec(t) csc(t) = ±1/sin(t) × 1/cos(t)

Multiplying the fractions gives us:

sec(t) csc(t) = 1 / (sin(t) × cos(t))

Now, recall the definition of tan(t) is sin(t)/cos(t). Hence:

sec(t) csc(t) = 1 / tan(t), which is the definition of cot(t).

Thus, the expression sec(t) csc(t) simplifies to cot(t).