Question

find cos 15° by using the formula cos(A-B) = cos Acos B+sin Asin B​

Answer 1

To find

The value of Cos15⁰

By Using

Cos(A - B) = CosACosB+SinASinB

Let

A = 60⁰ and B = 45⁰ Because A - B = 60⁰ - 45⁰ = 15⁰

So

Cos(60⁰ - 45⁰) = Cos60⁰Cos45⁰ + Sin60⁰Sin45⁰

We Know that

Cos60⁰ = 1/2

Cos45⁰ = 1/√2 = √2/2

Sin60⁰ = √3/2

Sin45⁰ = 1/√2 = √2/2

Now put the value on formula

Cos(60⁰ - 45⁰) = Cos60⁰Cos45⁰ + Sin60⁰Sin45⁰

Cos(60⁰ - 45⁰) = 1/2× √2/2 + √3/2×√2/2

Cos(60⁰ - 45⁰) = √2/4 + √6/4

Cos(60⁰-45⁰) = 1/4(√2 + √6)

So Value of Cos15⁰ = 1/4(√2 + √6)

Answer

Cos15⁰ = 1/4(√2 + √6)

Answer 2

To find

The value of Cos15⁰

By Using

Cos(A - B) = CosACosB+SinASinB

Let

A = 60⁰ and B = 45⁰ Because A - B = 60⁰ - 45⁰ = 15⁰

So

Cos(60⁰ - 45⁰) = Cos60⁰Cos45⁰ + Sin60⁰Sin45⁰

We Know that

Cos60⁰ = 1/2

Cos45⁰ = 1/√2 = √2/2

Sin60⁰ = √3/2

Sin45⁰ = 1/√2 = √2/2

Now put the value on formula

Cos(60⁰ - 45⁰) = Cos60⁰Cos45⁰ + Sin60⁰Sin45⁰

Cos(60⁰ - 45⁰) = 1/2× √2/2 + √3/2×√2/2

Cos(60⁰ - 45⁰) = √2/4 + √6/4

Cos(60⁰-45⁰) = 1/4(√2 + √6)

So Value of Cos15⁰ = 1/4(√2 + √6)

Answer

Cos15⁰ = 1/4(√2 + √6)