Question

Value of Tan 5°tan10°tan45°tan80°tan85° is

Answer 1

The value of$\tan 5.tan 10.tan 45.tan 80.tan 85$ is 1.

Step-by-step explanation:

We have,

$\tan 5.tan 10.tan 45.tan 80.tan 85$

$=\tan 5.tan 10.tan 45.tan(90-10).tan(90-5)$

$=\tan 5.tan 10.tan 45.cot10.cot5$

[ ∵ $tan(90-\theta)=\cot\theta$]

$=\(tan 5.cot 5).tan 45.(tan 10.cot 10)$

$=1.tan 45.1$

[∵$\tan \theta \times \cot \theta =1$]

= 1 [∵ $tan 45 =1$]

Hence, the value of$\tan 5.tan 10.tan 45.tan 80.tan 85$ is 1.

Answer 2

Step-by-step explanation:

tan5° tan40° tan45° tan50° tan85°

=tan5°× cot5°×tan40°×cot40°×tan45°

(°•° tanø=cot(90-ø))

=1

(°•° tanø.cotø=1,tan45°=1)