Without using trignometrical tables, prove that:
tan 10 .tan 15. tan 75 .tan 80 = 1
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Step-by-step explanation:
To prove :-
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
Hence proved.
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