Question

cos 75 degree + cos 15 degree

Answer 1

Hey there!

Answer:

√3 / √2   (without rationalizing)

√6/2   (after rationalizing)

Step-by-step explanation:

Given,

cos 75° + cos 15°

We know,

cos x + cos y = 2 cos(x+y)/2 * cos(x-y) / 2

cos(75 + 15)   = 2 cos(75+15)/2 * cos(75-15)/2

                       = 2cos(90/2) * cos(60/2)

                       = 2cos(45)*cos(30)

                       = 2*(1/√2)*(√3/2)

                       = √3 / √2

On rationalizing,                      

                      = (√6)/2

Hope It Helps You!

Answer 2

The value of cos75° + cos15° is √(3/2).

We have to find the value of cos75° + cos15°.

Use formula,

$cosA + cosB=2cos\left(\frac{A+B}{2}\right)cos\left(\frac{A-B}{2}\right)$

Here,

$cos75^{\circ} + cos15^{\circ}=2cos\left(\frac{75^{\circ}+15^{\circ}}{2}\right)cos\left(\frac{75^{\circ}-15^{\circ}}{2}\right)\\\\=2cos\left(\frac{90^{\circ}}{2}\right)cos\left(\frac{60^{\circ}}{2}\right)\\\\=2cos45^{\circ}cos30^{\circ}\\\\=2\times\frac{1}{\sqrt{2}}\times\frac{\sqrt{3}}{2}=\sqrt{\frac{3}{2}}$

Therefore the value of cos75° + cos15° is √(3/2).

Also read similar questions : show that cos 15 degree into cos 35 degree cosec 55 cos 60 degree cosec 75 degree =1/root2

https://brainly.in/question/6435939

integral of modulous of cosx in interval (0,2pi) https://brainly.in/question/9645

#SPJ3