Question

find the values of tan 10* tan 15* tan 75* tan 80*

Answer 1

tan10 tan15 tan(90-75) tan (90-80)
= tan10 tan15 cot 15 cot10
as we know tan theta * cot theta = 1
so
tan10 cot10 tan15 cot 15
= 1

Answer 2

Answer:

tan10×tan15×tan75×tan80=1

Step-by-step explanation:

Given,

tan10×tan15×tan75×tan80

Rearranging the terms, we get

=(tan10tan80)×(tan15tan75)

= [tan10tan(90-10)]×[tan15tan(90-15)]

= (tan10xcot10)×(tan15cot15)

/* We know that,

i ) tan(90-A) = cotA

ii) tanAcotA = 1 */

= 1 × 1

= 1

Therefore,

tan10×tan15×tan75×tan80=1

•••♪