Could someone explain the steps for this question.
Simplify the expression
tan(5pi/8)-tan(3pi/8)/1+tan(5pi/8)tan(3pi/8)
Options are
a) 0
b) 1
c) -1
d) undefined
Recall your sum/difference formulas. You have
tan(5pi/8-3pi/8) = tan(pi/4)
so, (B)
To simplify the given expression, follow these steps:
Step 1: Identify the formulas:
We will use the trigonometric identity for tangent: tan(A - B) = (tan A - tan B)/(1 + tan A tan B)
Step 2: Substitute the values:
Replace A with 5pi/8 and B with 3pi/8 in the formula:
tan(5pi/8 - 3pi/8) = (tan(5pi/8) - tan(3pi/8))/(1 + tan(5pi/8)tan(3pi/8))
Step 3: Simplify:
Simplify the expression by replacing the value of tan(5pi/8 - 3pi/8):
tan(2pi/8) = tan(pi/4)
Since the tangent of pi/4 is 1:
tan(pi/4) = 1
Substitute this value back into the expression:
1/(1 + tan(5pi/8)tan(3pi/8))
Step 4: Simplify further (if possible):
Simplification of the expression further is not possible without additional information.
Therefore, the simplified expression is:
1/(1 + tan(5pi/8)tan(3pi/8))