Questions -
Q1. Prove the following identities
a. sin(x + y) + sin(x - y) = 2 sin x cos y
b. sec(x - y) = cos(x + y)/(cos^{2}x - sin^{2}y)
c. tan^{2}x - sin^{2}x = (tan x sin x)^{2}
Q2. Solve the following equations for x ∈ [0, 2π] and verify the result using MATLAB.
a. tan x = cot x
b. 2 sin x + cot x - csc x = 0
c. 18 sec^{2}x - 17 tan x sec x - 12 = 0
Q3. Solve the following problems
a. A person standing in front of a building with a height of 50 m finds that the angle of elevation to the top of the building is 38^{o}. He then walks towards the building x m and finds the new angle of elevation to be 46^{o}. Calculate x.
b. A flying object is observed from two points on ground level that are on opposite sides of the object are 10 m apart. The angles of elevation from the two points to the object are 30^{o} and 40^{o}. Calculate the height of the object above the ground.
References -
1. McKeague, C. P., & Turner, M. D. (2013). Trigonometry. Australia: Brooks/Cole, Cengage Learning.
2. Lial, M. L. (2013). Trigonometry. Boston: Pearson.