Question

Cos pie divided by 12 in surd form

Answer 1

¼(√6 + √2)

Explanation:

We want to find cos (π/12) in surd form.

Now, cos (π/12) can be expressed as;

cos [(π/4) - (π/6)]

Now, from trig derivations we know that;

Cos (A - B) = CosACosB + sinAsinB

Thus;

cos [(π/4) - (π/6)] = cos(π/4)Cos(π/6) + sin(π/4)sin(π/6)

Now, in surd form;

cos(π/4) = sin(π/4) = (√2)/2

Cos(π/6) = (√3)/2

sin(π/6) = 1/2

Thus, Plugging in relevant values to get;

cos(π/4)Cos(π/6) + sin(π/4)sin(π/6) = ((√2)/2 × (√3)/2) + ((√2)/2 × 1/2)

This gives;

((√6)/4) + ((√2)/4) = ¼(√6 + √2)