4cos(x) = 3
solve this

41.4 degrees

Step-by-step explanation:

Find cos x by dividing both sides of this equation by 4:

cos x = 3/4 = 0.75

Using a calculator's inverse cosine function, find x:

arccos 0.75 = 0.723 radian, or

0.723 rad     180 deg

* = 41.4 degrees

        1             pi rad

The proof is mentioned below.

Step-by-step explanation:

Here, Δ ABC is isosceles triangle.

Therefore, AB = BC

Prove: Δ ABO ≅ Δ ACO

In Δ ABO and Δ ACO,

∠ BAO ≅ ∠ CAO  ( AO bisects ∠ BAC )

∠ AOB ≅ ∠ AOC ( AO is perpendicular to BC )

BO ≅ OC ( O is the mid point of BC)

Thus, By ASA postulate of congruence,

Δ ABO ≅ Δ ACO

Therefore, By CPCTC,

∠B ≅ ∠ C

Where ∠ B and ∠ C are the base angles of Δ ABC.