Without using the trigonometric table, prove that tan 10° tan 15°… - Vidyadip

Question

Without using the trigonometric table, prove that
tan 10° tan 15° tan 75° tan 80° = 1

✓

Answer

L.H.S. = tan 10° tan 15° tan 75° tan 80°
= tan 10° tan 15° tan (90° - 15°) tan (90° - 10°)
= = tan 10° tan 15° cot 15° cot 10°
$=\frac{1}{\cot 10}^{\circ} \times \frac{1}{\cot 15}^{\circ} \times \cot 15^{\circ} \times \cot 10^{\circ}$
= 1
= RHS
Hence proved.

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