Please help me........
1 answer:
Answer: see proof below
<u>Step-by-step explanation:</u>
Use the Sum/Difference Identity: tan (A + B) = (tanA + tanB)/(*1 - tanA · tanB)
Scratchwork:
tan (50) = tan (40 + 10)
tan 50 (1 - tan 40 · tan 10) = tan 40 + tan 10
tan 50 - tan 50 · tan 40 · tan 10 = tan 40 + tan 10
tan 50 = tan 40 + tan 10 + tan 50 · tan 40 · tan 10
Use the Reciprocal Identity: cot A = 1/ tan --> cot A · tan A = 1
<u>Proof LHS → RHS</u>
LHS: tan 50 - tan 40
Substitute tan 50: tan 40 + tan 10 + (tan 50 · tan 40) · tan 10 - tan 40
Simplify: tan 10 + (tan 50 · tan 40) · tan 10
Reciprocal Identity: tan 10 + tan 10
Simplify: 2 tan 10
LHS = RHS: 2 tan 10 = 2 tan 10
You might be interested in
Answer:
4. Z ≈ 46.1°
5. T ≈ 45.2°
6. F ≈ 15.0°
Step-by-step explanation:
4.
We need to use the Law of Sines, which states that for a triangle with legnths a, b, and c and angles A, B, and C:
Here, we can say that ZY = a = 30, X = A = 110, XY = b = 23, and Z = B. Plug these in to find Z:
Solve for Z:
Z ≈ 46.1°
5.
Use the Law of Sines as above.
Solve for T:
T ≈ 45.2°
6.
Again, use the Law of Sines as before.
Solve for F:
F ≈ 15.0°