Question

The value of the expression tan 10 tan20 tan 30 tan40 tha 870 tan88 tan890 is equal

Answer 1

Use concept of complementary angles

tan(90-x)=cot(x) and

cot(90-x)= tan(x)

so tan 80=tan (90–10)=cot(10)

similarly,

tan(70)=cot(20)

tan(60)=cot30)

tan(50)=cot(40)

So it simplifies to

tan(10)*cot(10)*tan(20)*cot(20)*tan(30)*cot(30)*tan(40)*cot(40)

Now you must be knowing that :P

tan(x)*cot(x)=1

So Ans comes out to be 1.

Thank you!!!

phew!!!

Answer 2

Your answer is 1

Hope this helps