1) Verify the following identities :
a) sin(x+y)cos(x-y) + cos(x+y)sin ( x-y) = sin 2x
b) cos2x = [cot^2 (x-1 )] / [ cot^2 (x+1) ]
2) Derive the identity for sin 3x in terms of sin x
3) Using the double-angle formula, find sin 120° .
4)Simplify the following expressions so that they involve a function of only one angle:
a) (sin 80° - sin 10° ) / (sin 80° + sin 10°)
b) (sin 130° + sin 20°) / (cos 130° + cos 20 °)
A) Use logarithms and the law of tangents to solve the triangle ABC,
given that a=21.46 ft, b=46.28 ft, and C=32° 28' 30"
B) Solve the triangle for which the given parts are :
a=27, b=21, and c=24
Neat, step-by-step solutions are provided for all the questions.