Find the value of tan 72° − tan 27° − tan 72° tan 27°.

Question

Accepted Answer

We need to find the value of tan 72° − tan 27° − tan 72° tan 27°.

Step 1: Recall the tangent subtraction formula:

tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

Step 2: Rearrange the given expression:

Given expression = tan 72° − tan 27° − tan 72° tan 27°

Rewrite it as:

= (tan 72° − tan 27°) − tan 72° tan 27°

Step 3: Consider the tangent subtraction formula for A = 72°, B = 27°:

tan(72° - 27°) = tan 45° = 1

Using the formula:

tan 45° = (tan 72° - tan 27°)/(1 + tan 72° tan 27°)

So,

tan 72° - tan 27° = 1 + tan 72° tan 27°

Step 4: Substitute this back into the expression:

Expression = (tan 72° − tan 27°) − tan 72° tan 27°

= (1 + tan 72° tan 27°) − tan 72° tan 27°

= 1

Therefore, the value of the expression is 1.

Answer

Answer

Answer