Question

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Answer 1

Answer:

3

Step-by-step explanation:

The key is to realize that when x + y = 90°, you have tan(x) tan(y) = 1.  To see this, draw a right angled triangle with angles x and y.  Then the side adjacent to the angle x is opposite the angle y, and vice versa.

Since cot(x) is just 1 / tan(x), the same thing holds there.  That is, when x + y = 90°, you have cot(x) cot(y) = 1.

Here we have

3 cot(31) tan(15) cot(27) tan(75) cot(63) cot(59)

= 3 × ( cot(31) cot(59) ) × ( tan(15) tan(75) ) × ( cot(27) cot(63) )

= 3 × 1 × 1 × 1 = 3,

since 31 + 59 = 90,  15 + 75 = 90 and 27 + 63 = 90.