COMEDK · Maths · 8. Trigonometric Ratios & Identities

\(\tan 10^{\circ} \tan 20^{\circ} \tan 30^{\circ} \tan 40^{\circ}\)
\(\tan 50^{\circ} \tan 60^{\circ} \tan 70^{\circ} \tan 80^{\circ}=\)

A 0
B \(-1\)
C \(\frac{1}{\sqrt{3}}\)
D 1

Verified Solution

Answer & Solution

Correct Answer

(D) 1

Step-by-step Solution

Detailed explanation

\(\tan 10^{\circ} \tan 20^{\circ} \tan 30^{\circ} \tan 40^{\circ} \tan 50\) \(\tan 60^{\circ} \tan 70^{\circ} \tan 80^{\circ}\) \(\quad=\tan 10^{\circ} \tan 20^{\circ}\left(\frac{1}{\sqrt{3}}\right) \tan 40^{\circ} \tan \left(90^{\circ}-40^{\circ}\right)\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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\(\tan 10^{\circ} \tan 20^{\circ} \tan 30^{\circ} \tan 40^{\circ}\)\(\tan 50^{\circ} \tan 60^{\circ} \tan 70^{\circ} \tan 80^{\circ}=\)

Step-by-step Solution

\(\tan 10^{\circ} \tan 20^{\circ} \tan 30^{\circ} \tan 40^{\circ}\)
\(\tan 50^{\circ} \tan 60^{\circ} \tan 70^{\circ} \tan 80^{\circ}=\)