Question

Simplify the expression
5⋅csc(θ)⋅tan(θ).

Answer 1

The expression 5⋅csc(θ)⋅tan(θ) simplifies to 5⋅sec(θ) after applying basic trigonometric identities where csc(θ) is the reciprocal of sin(θ) and tan(θ) is the ratio of sin(θ) over cos(θ).

Step-by-step explanation:

The question requires us to simplify the expression containing trigonometric functions 5⋅csc(θ)⋅tan(θ). To simplify this expression, we need to recall the basic trigonometric identity that links the cosecant and tangent functions:

csc(θ) = 1/sin(θ)

tan(θ) = sin(θ)/cos(θ)

When we multiply csc(θ) by tan(θ), we get:

5⋅csc(θ)⋅tan(θ) = 5⋅(1/sin(θ))⋅(sin(θ)/cos(θ)) = 5⋅(1/×cos(θ))

As sin(θ) cancels out, we are left with:

5⋅1/cos(θ) = 5⋅sec(θ)

Thus, the simplified expression is 5⋅sec(θ), which is the original expression multiplied by the secant of θ.