i posted this question up before but it didn't show up. anyways.. i need help determining whether these two statements are true or not. i tried converting them into square roots but never got the right answer. like cos30=square root 3/2. here they are
1. cos150deg+cos30deg=cos180deg
2. cos(30deg+90deg)=cos30degcos90deg-sin30degsin90deg
thankyou
1. definitely WRONG
cos(A+B) = cosAcosB - sinAsinB
which was used correctly in 2.
but would have been contradicted in 1.
ok thnks.
To determine whether these statements are true or not, let's understand the trigonometric identities involved and use them to simplify the expressions.
1. cos150° + cos30° = cos180°
To simplify this expression, we can use the trigonometric identity: cos(a + b) = cos(a)cos(b) - sin(a)sin(b).
So, using this identity:
cos150° + cos30° = cos(180°)
Now, cos(180°) = -1, so the equation becomes:
-1 + cos30° = -1
Since -1 and -1 are equal, the equation is true.
2. cos(30° + 90°) = cos30°cos90° - sin30°sin90°
To simplify this expression, we can again use the trigonometric identity: cos(a + b) = cos(a)cos(b) - sin(a)sin(b).
So, using this identity:
cos(30° + 90°) = cos(30°)cos(90°) - sin(30°)sin(90°)
Now, cos(90°) = 0 and sin(90°) = 1, so the equation becomes:
cos(30° + 90°) = cos30° * 0 - sin30° * 1
cos(30° + 90°) = -sin30°
Since cos(30° + 90°) = -sin30°, the equation is true.
Therefore, both statements are true.