Show that : tan 10° tan 15° tan 75° tan 80° = 1

1.	Show that : tan 10° tan 15° tan 75° tan 80° = 1
Answer» tan 10° tan 15° tan 75° tan 80° = 1 We will EXPAND the SAID values - = tan 10° tan 15° tan ( 90° - 15°) tan(90° - 10° ) = tan 10° tan 15° COT 15° cot 10° [ SINCE tan ( 90°-Ф = cot Ф) Thus after SUBSTITUTING the value - = tan 10° × 1 / tan 10° × tan 15° × 1 / tan 15° = 1 × 1 = 1

Answer»

tan 10° tan 15° tan 75° tan 80° = 1

We will EXPAND the SAID values -

= tan 10° tan 15° tan ( 90° - 15°) tan(90° - 10° )

= tan 10° tan 15° COT 15° cot 10° [ SINCE tan ( 90°-Ф = cot Ф)

Thus after SUBSTITUTING the value -

= tan 10° × 1 / tan 10° × tan 15° × 1 / tan 15°

= 1 × 1

= 1

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Show that : tan 10° tan 15° tan 75° tan 80° = 1

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