If 𝐴 = #sqrt(1+cos 320°)/2# and 𝐵 = #sqrt( 1−cos 320°)/ 2# , then 𝐴 + 𝐵 =?
If 𝐴 =
#sqrt(1+cos 320°)/2#
and 𝐵 = #sqrt(
1−cos 320°)/
2#
, then 𝐴 + 𝐵 =
a) 𝑐𝑜𝑠160° − 𝑠𝑖𝑛160°
b) −𝑐𝑜𝑠160° + 𝑠𝑖𝑛160°
𝑐) 𝑐𝑜𝑠160° + 𝑠𝑖𝑛160°
d) −𝑐𝑜𝑠160° − 𝑠𝑖𝑛160°
e) 0
If 𝐴 =
and 𝐵 =
, then 𝐴 + 𝐵 =
a) 𝑐𝑜𝑠160° − 𝑠𝑖𝑛160°
b) −𝑐𝑜𝑠160° + 𝑠𝑖𝑛160°
𝑐) 𝑐𝑜𝑠160° + 𝑠𝑖𝑛160°
d) −𝑐𝑜𝑠160° − 𝑠𝑖𝑛160°
e) 0
1 Answer
The correct answer is
I cannot see the choices while answering so please find the corresponding letter.
Explanation:
Where we run into trouble is with signs. To get out of trouble we use the symmetry relations of trigonometric functions to get the argument between 0° and 90°.
We start with
Then
Now apply the half angle formulas:
By making the argument between 0° and 90°, we assure tgat both signs are positive and thus we beat the sign problems:
So
Now we can get an angle of 160° using these symmetry relations:
Then
I cannot see the multiple choices whilevwriting the answer so please pick the right letter accordingly.