Question

Solve this please
please​

Answer 1

Explanation:

cos(2a) = cos^2(a) - sin^2(a)

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

cos(2a) = 11/25

11/25 = 2 cos^(a) - 1 Add 1 to both sides

1 + 11/25 = 2 cos^2

25/25 + 11/25 = 2 cos^2(a)

36/25 = 2 cos^2 (a) Divide by 2

36/50 = cos^2 (a) Take the square root of both sides.

6/5*sqrt(2) = cos(a)

Answer 2

One is given the following:

• 
  `cos(2A)=(11)/(25)`

One is asked to prove the following:

• 
  `cos(A)=(6)/(5√(2))`

In order to prove the statement above, one will need to use a trigonometric identity. In this case, the following identity is the most relevant in the proof.

`cos(2a)=2cos^2(A)-1`

One can manipulate this identity to suit the needs of the given problem:

`cos(2a)=2cos^2(A)-1`

`cos(2a)+1=2cos^2(A)`

`(cos(2a)+1)/(2)=cos^2(A)`

`\sqrt{(cos(2a)+1)/(2)}=cos(A)`

Now substitute the given information into this identity,

`cos(2A)=(11)/(25)`

`\sqrt{(cos(2a)+1)/(2)}=cos(A)`

Substitute,

`\sqrt{((11)/(25)+1)/(2)}=cos(A)`

Simplify, remember, any number over itself equals (1) and, in order to add two fractions, they must have the same denominator.

`\sqrt{((11)/(25)+1)/(2)}=cos(A)`

`\sqrt{((11)/(25)+(25)/(25))/(2)}=cos(A)`

`\sqrt{((36)/(25))/(2)}=cos(A)`

`\sqrt{(18)/(25)}=cos(A)`

`(3√(2))/(5)=cos(A)`

Manipulate so that it resembles the given information; remember, any number over itself is (1), multiplying an equation by (1) doesn't change it,

`(3√(2))/(5)=cos(A)`

`(3√(2))/(5)*(√(2))/(√(2))=cos(A)`

`(3√(2*2))/(5*√(2))=cos(A)`

`(6)/(5√(2))=cos(A)`