Question

Is the work shown in the simplification below correct? Explain. csc(t) sec(t) = 1 cos(t) ÷ 1 sin(t) = 1 cos(t) • sin(t) 1
= 1 sin(t)
= tan(t)

Answer 1

No, because it states csc(t) x sec(t), not divide, so therefore it would result to (1/cos(t)) x (1/sin(t)) if simplified 

Answer 2

The given product is not equal to 1, hence the work shown in the simplification is NOT correct

Given the expression;

• $csc(t)\cdot sec(t) = 1$

According to trigonometry identity;

• csc(t) = 1/sin(t)
• sec(t) = 1/cos(t)

Substituting into the expression to check if true, we will have:

$\frac{1}{sin(t)} \cdot \frac{1}{cos (t)} = \frac{1}{sin(t)cos(t)} \neq 1$

Since the given product is not equal to 1, hence the work shown in the simplification is NOT correct

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