Simplifying Trig

Question

0

1073

3

+1252

The expression is $4cos40cos50-4sin27.5sin17.5$ (in degrees.)

I got 0, with the following strategy

$4[1/2(cos10+cos90)]-4[\frac{1}{2}(cos10-cos45)$ using product identities and then

$2cos10+2cos90-2cos10-2cos90=0$

But when I plug it in a calculator it shows up as $\sqrt2$ .

Help please?

Thank you very much!

:P

CoolStuffYT Jun 15, 2019

Guest · Answer 1 · 2019-06-15T02:18:13

Just wrong with the final term, which should be +2cos(45).

CPhill · Answer 2 · 2019-06-15T06:22:58

4cos (50) cos(40) - 4sin(27.5)sin(17.5)

2 [2cos(50) cos(40) - 2sin (27.5)sin(17.5) ] =

2 [ cos (50 - 40) + cos (50 + 40) - [ cos (27.5 - 17.5) - cos(27.5 + 17.5) ] ] =

2 [ cos(10) + cos(90) - cos(10) +cos(45) ] =

2cos(90) + 2cos(45) =

0 + 2√2 / 2 =

√2