Suppose that tanalpha =3 and 0^circ lt alpha lt 90^circ Find the exact values of cos(alpha )/(2) and tan(alpha )/(2) cos(alpha )/(2)= tan(alpha )/(2)= square

Question

Answer 1

To find the exact values of

and

, we can use the half-angle formulas.Given that

and

, we can find the value of

and

using the Pythagorean identity

.Since

, we can let

and

. Substituting these values into the Pythagorean identity, we get:

Therefore,

and

.Now, let's find

and

using the half-angle formulas.The half-angle formula for cosine is:

Since

, we know that

. Therefore,

is positive.Substituting the value of

, we get:

Simplifying further, we have:

The half-angle formula for tangent is:

Again, since

, we know that

. Therefore,

is positive.Substituting the values of

and

, we get:

Simplifying further, we have:

Therefore, the exact values of

and

are:

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