Question

Sin77*sin88+cos77*cos88

**HELP ASAP**

Note: Numbers next to functions are in degrees.

Answer 1

`\sf cos(77) * cos(88) + sin(77) * sin(88) =\boxed{\sf cos(11) \approx 0.982}`

Explanation:

To simplify the expression
`\sf sin(77) * sin(88) + cos(77) * cos(88)`, we'll use trigonometric identities.

The identity we'll use is the product-to-sum formula for cosine:

`\boxed{\sf cos(A - B) = cos(A) * cos(B) + sin(A) * sin(B)}`

Now, let A = 77 and B = 88

`\sf cos(77 - 88) = cos(77) * cos(88) + sin(77) * sin(88)`

Notice that 77 - 88 = -11 degrees.

`\sf cos(-11) = cos(77) * cos(88) + sin(77) * sin(88)`

Now, we know that cos(-x) = cos(x), so:

`\sf cos(11) = cos(77) * cos(88) + sin(77) * sin(88)`

Finally, since the cosine function is even (cos(x) = cos(-x)), we have:

`\sf cos(11) = cos(77) * cos(88) + sin(77) * sin(88) = cos(-11)`

Therefore:

`\sf cos(77) * cos(88) + sin(77) * sin(88) =\boxed{\sf cos(11) \approx 0.982}`

See the attachment for trigonometric identities formula: