The expression (csc(t))/(sec(t)) simplifies to sin(t) × cos(t), using the fact that csc(t) is the reciprocal of sin(t) and sec(t) is the reciprocal of cos(t).
Step-by-step explanation:
To simplify the expression (csc(t))/(sec(t)) to a single trigonometric function without fractions, we can use basic trigonometric identities. The cosecant function, csc(t), is the reciprocal of the sine function, so csc(t) = 1/sin(t). The secant function, sec(t), is the reciprocal of the cosine function, so sec(t) = 1/cos(t). The expression we want to simplify is therefore:
(1/sin(t)) / (1/cos(t))
We can simplify this by flipping the divisor and multiplying:
sin(t) × cos(t)
This is equivalent to the trigonometric identity for sin(2t)/2, but you just need to use sine and cosine directly. Therefore, the simplified expression is:
sin(t) × cos(t)
The probable question can be: Simplify (csc(t))/(sec(t)) to a single trig function with no fractions.