Question

prove tan6tan42tan66tan78=1

Answer 1

You see, there’s a law that says

tan(x) * tan(60 + x) * tan(60 - x) =tan(3x)

We’ll use that law

tan6 * tan42 * tan66 * tan78 =

tan 6 * tan66 * tan54 * tan18 * tan78 * tan42 / (tan 18 * tan 54)

since tan 6 * tan 66 * tan 54 = tan 18, tan 18 * tan 42 * tan 78 = tan 54

the denominator equals the numerator

so it equals 1

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Answer 2

Answer:

We’ll use the law : tan(x) * tan(60 + x) * tan(60 - x) =tan(3x)

tan6 * tan42 * tan66 * tan78 =

tan 6 * tan66 * tan54 * tan18 * tan78 * tan42 / (tan 18 * tan 54)

since tan 6 * tan 66 * tan 54 = tan 18, tan 18 * tan 42 * tan 78 = tan 54

so it equals 1