The formula or the identity of the product sinx cosy is obtained by the transformation of sums or differences of trigonometric angles. sinx cosy formula is given below.

sinx cosy = $\dfrac{\sin(x+y)+\sin(x-y)}{2}$

## Proof of sinx cosy Formula

Let us now prove the sinx siny formula

sinx cosy = $\dfrac{\sin(x+y)+\sin(x-y)}{2}$

*Proof:*

It is known that

sin(x+y) = sinx cosy + cosx siny **…(I)**

sin(x-y) = sinx cosy – cosx siny **…(II)**

Adding **(I)** and **(II)**, we obtain that

sin(x+y) + sin(x-y) = (sinx cosy + cosx siny) + (sinx cosy – cosx siny)

⇒ sin(x+y) + sin(x-y) = sinx cosy + cosx siny + sinx cosy – cosx siny

⇒ sin(x+y) + sin(x-y) = 2sinx cosy

Dividing both sides by 2, we get that

sinx cosy = $\dfrac{\sin(x+y)+\sin(x-y)}{2}$

So the formula of sinx cosy formula is given as follows: sinx cosy= 1/2 [sin(x+y) + sin(x-y)].

**sinx cosy Formula:**

$\sin x \cos y = \dfrac{\sin(x+y)+\sin(x-y)}{2}$ |

**ALSO READ:**

## Application of sinx cosy Formula

**Question 1: **Find the value of sin45 cos15.

*Answer:*

By the above formula with x=45 and y=15, we will obtain that

sin45 cos15 = $\dfrac{\sin(45+15)+\sin(45-15)}{2}$

= $\dfrac{\sin 60+\sin 30}{2}$

= $\dfrac{\frac{\sqrt{3}}{2} +\frac{1}{2}}{2}$

= $\dfrac{\frac{\sqrt{3}+1}{2}}{2}$

= $\dfrac{\sqrt{3}+1}{4}$

Thus, the value of sin45 cos15 is equal to (√3+1)/4.

## FAQs

**Q1: What is the formula of sinx cosy?**

**Answer:** The formula of sinx cosy is equal to sinx cosy = 1/2 [sin(x+y)+sin(x-y)].

**Q2: What is the formula of sina cosb?**

**Answer:** The formula of sina cosb is given by sina cosb = 1/2 [sin(a+b)+sin(a-b)].

**Q3: What is the formula of 2sinx cosy?**

**Answer:** The formula of 2sinx cosy is given by 2sinx cosy = sin(x+y)+sin(x-y).

**Q4: What is the formula of 2sina cosb?**

**Answer:** The formula of 2sina cosb is given by 2sina cosb = sin(a+b)+sin(a-b).