Question

value of tan5° tan10° tan15° tan20° till tan85°

Answer 1

tan 85 = cot (90-5) = cot 5
tan 5*cot 5=1
This will happen for all pairs except 45
So answer is tan 45=1
So, the final answer is 1

Answer 2

tan 5° tan 10° tan 15° ................. tan 75° tan 80° tan 85°
______________________________________________________

= tan 5° tan 10° tan 15°.................tan(90-15)° tan(90-10)° tan(90-5)°

= tan 5° tan 10° tan 15° ................cot 15° cot 10° cot 5°

As tanΘ × cotΘ = 1

Then,

= 1 
______________________________________________________

☺ ☺ ☺ Hope this Helps ☺ ☺ ☺