Question

prove that cos1° is an irrational number
pls answer it fast ​

Answer 1

Answer:

Proof of irrationality of cos(1∘)

Step-by-step explanation:

Assume for the sake of contradiction, that cos(1∘) is rational. Since,

cos(2∘)=2cos2(1∘)−1

we have that, cos(2∘) is also rational. Note that, we also have

cos(n∘+1∘)+cos(n∘−1∘)=2cos(1∘)⋅cos(n∘)

By Strong induction principle, this shows that cos(n∘) is rational for all integers n≥1. But, this is clearly false, as for instance, cos(30∘)=3–√2 is irrational, reaching a contradiction.

But, as my title suggests, sin(1∘) is irrational, (look at the following image for its value!)Sine 1 degree