Question Video: Using Sum-to-Product Identities Mathematics

Video Transcript

Write the expression sin of 80 plus sin of 20 as a product of trigonometric expressions.

The expression sin of 80 plus sin of 20 is the sum of two trig functions. And we’re being told to write this as a product, which means we’ll need to use sum-to-product identities. And from them, we can say that sin of 𝑎 plus sin of 𝑏 is equal to two times sin of 𝑎 plus 𝑏 over two times cos of 𝑎 minus 𝑏 over two. For us, 𝑎 is equal to 80 and 𝑏 is equal to 20.

We’ll substitute in the values of 80 and 20 into this identity, which will give us two times sin of 80 plus 20 over two times cos of 80 minus 20 over two. 80 plus 20 is 100. 100 divided by two is 50. 80 minus 20 equals 60 divided by two is 30, which means sin of 80 plus sin of 20 will be equal to two times sin of 50 times cos of 30. And two sin 50 cos 30 is a product of trigonometric expressions.