Question

prove that (1+tan10)(1+tan20)(1+tan25)(1+tan35)=4

Answer 1

Answer:

Answer...

Step-by-step explanation:

It is certainly true that

1+tan10°=sin10°+cos10°cos10°=(2–√)(sin(10°+45°)cos10°)

where sin(10°+45°)=(sin10°/2–√)+(cos10°/2–√) from the formula for the sine of a sum. Then, continuing:

1+tan10°=(2–√)(sin(10°+45°)cos10°)=(2–√)(cos35°cos10°)

using sin(10°+45°)=cos(90°−10°−45°)=cos35°. Do the same with arguments of 20°,25°,35° in place of 10° and multiply the four resulting fractions together; all the trig functions cancel out of the product and you have just (2–√)4=4.

The business with A,B,C, however, has me completely stumped. It does not enter the above equality at all!