Find the e xact value of cos75^circ cdot sin15^circ

Question

Find the e xact value of cos75^circ cdot sin15^circ

Answer 1

To find the exact value of

, we can use trigonometric identities and properties. Specifically, we will use the product-to-sum identities and the angle subtraction formulas.First, recall the product-to-sum identity for cosine and sine:

Here,

and

. Applying the identity, we get:

Simplify the arguments of the sine functions:

We know that:

Substituting these values back into the expression, we have:

Simplify the expression inside the brackets:

Now, multiply by

:

Thus, the exact value of

is:

Question

Find the e xact value of cos75^circ cdot sin15^circ

Solution

Resposta