Question

Evaluate tan 5 tan 25 tan 30 tan 65 tan 85

Answer 1

Answer:

1/√3

Step-by-step explanation:

use complementary ratios...& reciprocal ratios

tan ( 90-@) = cot @ & cot @ = 1/tan @

hence....tan ( 90-@) = 1/tan @

i,e tan ( 90-@) ( tan @ ) = 1

now rearrange....

tan 5 tan 25 tan 30 tan 65 tan 85

= ( tan 5 tan 85 ) ( tan 25 tan 65 ) tan 30

= [ tan 5 tan (90-5) ] [ tan 25 tan (90-25) ] tan 30

= ( 1 ) ( 1 ) tan 30

= tan 30°

= 1/√3