Question

Solve tan6°tan42° tan66°tan78°=1

Answer 1

Dear Student:

Use, $tanxtan(60+x)tan(60-x)=tan3x$

Let,x =18

Then,$tan18tan(60+18)tan(60-18)=tan3*18$

$tan18tan(78)tan(42)=tan54$

$tan78tan42=\frac{tan54}{tan18}$........(i)

If x=6

$tan6tan(60+6)tan(60-6)=tan3*6$

$tan6tan(66)tan(54)=tan18$

$tan6tan66=\frac{tan18}{tan54}$..........(ii)

Hence, by multiplying i) and ii)

tan6°tan42° tan66°tan78°=1

Answer 2

Answer:Step-by-step explanation:tan(90°-78°).tan(90°-66).tan66°.tan78=1

cot78°.cot66°.tan66°.tan78°=1

cot78°.tan78°.cot66°.tan66°=1

1×1=1

Step-by-step explanation: