Question

the value of tan 15 tan 20 tan 75 tan 70 is

Answer 1

tan 15 tan 20 tan 75 tan 70
tan(90-x)= cot x
tan 15=cot 75
tan20=cot 70
tan75cot75=1
tan70cot70=1
so answer is 1

Answer 2

Answer:

Explanation:

First collect the ratios to make 90

i.e,tan15*tan75*tan20*tan70

Now use identity to samaller angle

Cot(90-15)tan75*Cot(90-20)tan70

Cot75*tan75*Cot70*tan70

We know cot=cos/sin and Tan=sin/cos. Then use this to get,

Cos75/sin75*sin75/cos75*

Cos70/sin70*sin70/tan70

All cut together

We get, 1*1=1