Question

Given that cos(a-b)=cosacosb+sinasinb find the value of cos15

Answer 1

Step-by-step explanation:

Cos(45-30)

=Cos45 sin30 - cos30 sin45

=1/√2*1/2 - √3/2*1/√2

=(1-√3)/2√2

Answer 2

Answer:

The value of cos(15) is $\dfrac{\sqrt3+1}{\sqrt2}$

Step-by-step explanation:

Given that,

• cos(a-b)=cos(a)cos(b) + sin(a)sin(b) -------------(i)

we have to find the value of cos(15)

So, let us take,

• a = 45
• b = 30

Now,put the above values in equation-(i), equation-(i) becomes-

cos(a-b)=cos(a)cos(b) + sin(a)sin(b)

cos(45-30)=cos(45)cos(30) + sin(45)sin(30) ---------------(ii)

where,

• cos(45) = $\dfrac{1}{\sqrt{2}}$
• cos(30) = $\dfrac{\sqrt{3}}{2}$
• sin(45) =  $\dfrac{1}{\sqrt{2}}$
• sin(30) = $\dfrac{1}{2}$

Put the above values in equation-(ii)

cos(15) = $\dfrac{1}{\sqrt{2}}\times\dfrac{\sqrt{3}}{2} + \dfrac{1}{\sqrt{2}}\times\dfrac{1}{2}$

cos(15) = $\dfrac{\sqrt3+1}{\sqrt2}$