Question

simplify the expression by writing it in terms of sines and cosines, then simplify. the final answer does not have to be in terms of sine and cosine only. cot2(x) cos(x) sec(x)

Answer 1

The original expression cot^2(x) cos(x) sec(x) simplifies to cos(x) × csc^2(x), which is achieved by substituting trigonometric identities for cot(x) and sec(x) and then simplifying to get the expression in terms of sine and cosine.

Step-by-step explanation:

The expression provided is cot2(x) cos(x) sec(x). To simplify this expression, we need to write it in terms of sines and cosines and then simplify further. We know that cot(x) = cos(x)/sin(x) and sec(x) = 1/cos(x).

Substituting these definitions into the original expression gives us:

(cos2(x)/sin2(x)) × cos(x) × (1/cos(x))

Simplifying, the cos(x) in the numerator and the denominator cancel out, leaving us with:

cos(x)/sin2(x)

Further simplifying by splitting the fraction, we get:

cos(x) × (1/sin(x)) × (1/sin(x))

Finally, we know that 1/sin(x) is csc(x), thus:

cos(x) × csc2(x) is the simplified expression.