Question

The value of (tan1° tan2° tan3° ... tan89°) is (A) 0 (B) 1 (C) 2 (D) 1/2

Answer 1

Answer:

Step-by-step explanation:

tan1 * tan89 = 1

tan2 * tan88 = 1

tan3 * tan 87 = 1

and so on intill

tan44 * tan 46 = 1

now

tan1 * tan2 * ...* tan45 * ... * tan88 * tan89 = tan45 = 1

Answer 2

the correct answer is 1
we know that tan1 theta=tan(90-89)theta=cot 89 theta
so,tan2 theta=cot 88 theta and tan 3 theta= cot 87 theta
Now,
=A/q, tan1 tan2 tan 3.......tan87 tan 88, tan 89.
=cot89 cot88 cot 87............tan 87 tan 88 tan 89.
=1/tan87 1/tan 88 1/tan87.....tan87 tan88 tan89.
=1