1+tan13°)(1+tan32°) / (1+tan12°)(1+tan33°)=

Explanation:

To evaluate the expression:

(1 + tan 13°)(1 + tan 32°) / (1 + tan 12°)(1 + tan 33°),

we use the trigonometric identity:

(1 + tan A)(1 + tan B) = 2

This identity holds when A + B = 45°.

Step-by-Step Solution

Numerator:

• A = 13°
• B = 32°

Since 13° + 32° = 45°, we apply the identity:

(1 + tan 13°)(1 + tan 32°) = 2

Denominator:

• A = 12°
• B = 33°

Since 12° + 33° = 45°, we apply the identity:

(1 + tan 12°)(1 + tan 33°) = 2

Final Calculation:

Now substitute the results into the original expression:

(1 + tan 13°)(1 + tan 32°) / (1 + tan 12°)(1 + tan 33°) = 2 / 2 = 1

Final Answer

The value of the expression is: 1