Question

The value of tan10º tan15º tan75º tan80º is

• A. –1
• B. 0
• C. 1
• D. None of these

Answer 1

The Correct Option is C

Given: \( \tan 10^\circ \tan 15^\circ \tan 75^\circ \tan 80^\circ \)

Step 1: Use the identity 

\[ \tan x \tan (90^\circ - x) = 1 \] Applying this identity: \[ \tan 10^\circ \tan 80^\circ = 1 \] \[ \tan 15^\circ \tan 75^\circ = 1 \]

Step 2: Multiply the expressions

\[ (\tan 10^\circ \tan 80^\circ) \times (\tan 15^\circ \tan 75^\circ) = 1 \times 1 = 1 \]

Final Answer: 1