Find the exact value cos (-15)?

cos(A - B) = cosAcosB + sinAsinB

so, cos(45 - 60) = cos45cos60 + sin45sin60

i.e. (√2/2)(1/2) + (√2/2)(√3/2)

=> (1/4)(√2 + √6)

:)>

same as cos(15 degrees)...

basically, cos^2(15) = cos^2(30/2) = (1 + cos(30))/2 (the half-angle identity)
cos(30) = sqrt(3)/2
so cos^2(30) = (1+ sqrt(3)/2)/2 = (2+ sqrt(3))/4
Finish from there.

For all values of the angle A we know that, 

(sin A/2 + cos A/2)² = sin² A/2 + cos² A/2 + 2 sin A/2 cos A/2 = 1 + sin A

Therefore, sin A/2 + cos A/2 = ± √(1 + sin A), [taking square root on both the sides]

Now, let A = 30° then, A/2 = 30°/2 = 15° and from the above equation we get,

sin 15° + cos 15° = ± √(1 + sin 30°) ….. (i)

Similarly, for all values of the angle A we know that, 

(sin A/2 - cos A/2)² = sin² A/2 + cos² A/2 - 2 sin A/2 cos A/2 = 1 - sin A

Therefore, sin A/2 - cos A/2 = ± √(1 - sin A), [taking square root on both the sides]

Now, let A = 30° then, A/2 = 30°/2 = 15° and from the above equation we get,

sin 15° - cos 15°= ± √(1 - sin 30°) …… (ii)

Clearly, sin 15° > 0 and cos 15˚ > 0

Therefore, sin 15° + cos 15° > 0

Therefore, from (i) we get,

sin 15° + cos 15° = √(1 + sin 30°) ..... (iii)

Again, sin 15° - cos 15° = √2 (1√2 sin 15˚ - 1√2 cos 15˚)

or, sin 15° - cos 15° = √2 (cos 45° sin 15˚ - sin 45° cos 15°)

or, sin 15° - cos 15° = √2 sin (15˚ - 45˚)

or, sin 15° - cos 15° = √2 sin (- 30˚)

or, sin 15° - cos 15° = -√2 sin 30°

or, sin 15° - cos 15° = -√2 ∙ 12

or, sin 15° - cos 15° = - √22

Thus, sin 15° - cos 15° < 0

Therefore, from (ii) we get, sin 15° - cos 15°= -√(1 - sin 30°) ..... (iv)

Now, subtracting (iv) from (iii) we get,

2 cos 15° = √ (1+1/2)  + √ (1-1/2)

2 cos 15° = (√ 3 +1)/√ 2

cos 15° =  (√ 3 +1)/2√ 2

.......            .........      (√ 3 +1)
Therefore, cos 15° = -----------  
............................        2√ 2

This value corresponds to the angle ( + 15°)  that is in the first Quadrant.

Angle (-) 15° falls in the fourth quadrant. In this quadrant too the sign of the cos value 

is the same as in the First quadrant. Hence --

...................  (√ 3 +1).
cos (-15°) = ------------ ....................... Answer
......          ..... .2√ 2

cos (-15°) = 0.9659258  ....... Answer

Mistake: -15 is in degrees or in radians? If in degrees, then
cos(-15*)=
cos(15*)=
cos(45*-30*)=
cos(45*)cos(30*)+sin(45*)sin(30*)=?
you complete it.

Trigonometric identities used:
cos(-θ) = cos(θ)
cos²(θ/2) = (1 + cosθ)/2

cos(-15°)
= cos(15°)
= √{[1 + cos(30°)]/2} ...... for cos(15°) > 0
= √{[1 + (√3/2)]/2}
= √[(1/2) + (√3/4)]

Cos -15° = 0.96592582628

Do you know this identity?

cos(a - b) = cos(a).cos(b) + sin(a).sin(b) → suppose that: a = 45

cos(45 - b) = cos(45).cos(b) + sin(45).sin(b) → suppose that: b = 30

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

cos(15) = [(√2)/2].[(√3)/2] + [(√2)/2].(1/2)

cos(15) = [(√6)/4] + [(√2)/4]

cos(15) = (√6 + √2)/4 → recall: cos(x) = cos(- x)

cos(- 15) = (√6 + √2)/4

It makes sense that this is in degrees, as it would be hard to find the cos of something in radians that didn't have pi in it.  Perhaps that was stated elsewhere in the problem.

Remember that cos(-x) = cos(x).  So this is the same as cos(15 degrees).

Remember the double angle formula, which you can look up, or derive from the cos(a+b) formula.  It is

cos(2x) = 2cos^2(x) - 1

cos(30) = 2 cos^2(15) - 1

cos(30) we can get from the 30-60-90 triangle, with sides of 1, 1/2, and sqrt(3)/2, the last one being the cos(30).  Sketch it out if unsure.

So

sqrt(3) / 2 = 2 (cos(15))^2 - 1

and solve for cos(15)

buy a calculator

1.   cos (2x) = 2 cos^2 x - 1
2.   cos (-x) = cos x
(I take it that you mean  -15 degrees.
Without the unit specifier,  -15 radians is implied, except perhaps in colloquial speech   .)

cos (-15 deg) = cos (15 deg) ,
   which > 0 .
cos^2 (-15 deg)  (1/2) (cos (30 deg) + 1)
    = (1/2) (√3/2 + 1)
    = (1/4) (4 + 2√3) .
    = ( (1/2) (√3 + 1) )^2
So  cos (-15 deg) = (1/2) (√3 + 1) .

cos(2x) = 2cos^2(x) -1. Put x = -15. Then cos(-30) = 2cos^2(-15) -1 = (1/3)rt3. Now cos(y) = 
cos(-y). Therefore cos(-15) = cos(15). cos^2(15) = (1/2)(1 +(1/3)rt3) = (1/6)(3+rt3);
Exact value of cos (-15) = ((3+rt3)/6)^(1/2).

cos (-15) = cos 15 = (√6+√2)/4

-15 means -15° ? If so, then
cos(-15°) 
= cos(45° - 60°)
= cos45°cos60° + sin45°sin60°
= ((√2)/2)(1/2) + ((√2)/2)((√3)/2)
= (√2)/4 + (√6)/4
= (√2 + √6)/4

.9659                                                  ,