Question

prove that'
tan10*tan30*tan50*tan70=1/3

Answer 1

Answer:

Step-by-step explanation:

tan10*tan30*tan50*tan70

=tan10*1/root3*tan(60-10)*tan(60+10)

=tan10*1/root3*tan60-tan10/1-tan60tan10*tan60+tan10/1-tan10tan60

=tan10*1/root3*3-tan^10/1-3tan^210

=1/root3*3tan10-tan^310/1-3tan^2

=1/root3*tan3(10)

1/root3*1/root3

=1/3