Question

-
(i) tan 10° tan 15° tan 75° tan 80° =1​

Answer 1

Answer:

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.