Question

Question #f4251

Answer 1

Use the formula `cos(90°-theta)=sintheta` and `sin2theta=2sinthetacostheta`.

Explanation:

Here is the proof:

`2cos70°cos20°`
`=2cos(90°-20°)cos20°`
`=2sin20°cos20°`
`=sin(2*20°)`
`=sin40°`
`=cos(90°-40°)`
`=cos50°`.

Or, there is another formula.
`2cosalphacosbeta=cos(alpha+beta)+cos(alpha-beta)`

Then,
`2cos70°cos20°`
`=cos(70°+20°)+cos(70°-20°)`
`=cos90°+cos50°`
`=cos50°`.