How do you write $cos 75 cos 35 + sin 75 sin 35$ $cos75cos35+sin75sin 35$ as a single trigonometric function?

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Answer 1 · 2015-02-03T09:25:33

The answer is: $cos 40$ $cos40$ .

It is easy if we remember the angle difference formula of cosine, that says:

$cos (α - β) = cos α cos β + sin α sin β$ $cos(alpha-beta)=cosalphacosbeta+sinalphasinbeta$ .

In this case $α = 75$ $alpha=75$ and $β = 35$ $beta=35$ , and we can use the formula conversely:

$cos 75 cos 35 + sin 75 sin 35 = cos (75 - 35) = cos 40$ $cos75cos35+sin75sin35=cos(75-35)=cos40$ .

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