Question

The value of cos 30x cos 60 + sin 30 x sin 60 =
​

Answer 1

Answer:

We know that

cos 60= 1/2

cos 30= √3/2

sin 60= √3/2

sin 30=1/2

Substituting all the values in the given equation we get

1/2 + √3/2 + √3/2 + 1/2

= √3/4 + √3/4

= 2√3/4

= √3/2

Answer

cos 60∘× cos 30∘+sin 60∘× sin30∘= √3/2

Answer 2

Answer:

$\sf\dfrac{\sqrt{3}}{2}$

Step-by-step explanation:

Given,

$\sf cos30\degree\times cos60\degree + sin30\degree\times sin60\degree$

Solution :-

Method 1 :-

$cos30\degree = \dfrac{\sqrt{3}}{2}$

$cos60\degree = \dfrac{1}{2}$

$sin30\degree = \dfrac{1}{2}$

$sin60\degree = \dfrac{\sqrt{3}}{2}$

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

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

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

$= \dfrac{2\sqrt{3}}{4}$

$= \dfrac{\sqrt{3}}{2}$

Method 2 :-

cosAcosB + sinAsinB = cos(A - B)

$\sf cos30\degree\times cos60\degree + sin30\degree\times sin60\degree = cos(30 - 60)$

= $\sf cos(-30\degree)$

= $\sf cos30\degree$

= $\sf\dfrac{\sqrt{3}}{2}$