Use the diagram to complete the statements about how to prove the cosine sum identity. A unit circle. Point P is on the circle o
n the x-axis at (1, 0). Point S is in quadrant 4 on (cosine (negative beta), sine (negative beta) ). Point Q is in quadrant 1 above point P at (cosine (alpha), sine (alpha) ). Point R is above point Q at (cosine (alpha + beta), sine (alpha + beta) ). Triangles AOC and BOD are congruent by SAS. Therefore, and these lengths can be found using the . Because this is the unit circle, the coordinates of points A, B, and D are equal to cosine and sine of Alpha + Beta , Alpha, and –β, respectively. Write expressions for the lengths and set them equal. Rewrite cos(-Beta) and sin(-Beta) using the identities before squaring both sides of the equation. Simplifying the resulting expressions involving cosine and sine of Alpha, Beta, and Alpha + Beta requires using the identity. When simplified, the equation becomes cos(Alpha + Beta) = cos(Alpha)cos(Beta) - sin(Alpha)sin(Beta).
2 answers:
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Answer:
To decide whether to add or subtract, determine if the values of the coefficients are the same or opposites:
. If the values are the same, subtract the equations.
• If the values are opposites or additive inverses, add the equations.
Step-by-step explanation:
Given
Required
How to solve
Options (1) and (2) are incorrect because none of the options eliminate x or y.
For option (3),
- Check for the coefficients of x and y
- If they are the same (sign and value), then subtract; otherwise add
For instance:
Rewrite the second equation
The coefficient of y are the same, so we subtract;
<em>See that y has been eliminated</em>