Sin (A + B )≡sin Acos B+cosAsinB, sin (A −B )≡sin Acos B-cosAsinB.

a)Prove that . sin (A + B )+sin (A −B ) ≡ 2sinAcosB.

b)Hence Prove that sin P +sin Q≡ 2sin ((P + Q)/2)cos ((P -Q)/2)

(c ) Hence or otherwise , show that sin 5θ+ 2sin3θ +sin θ ≡ 4 sin3θ 〖cos〗^2 θ

(d ) Solve to the nearest 0.1º , for 0º ≤ θ ≤ 90º ,the equation

sin 5θ + 2sin 3θ +sin θ = 3〖cos〗^2 θ

Acompany manufactures large valves, packed in boxes. a shipment consists of 1500 valves packed in 75 boxes. each box has the outer dimensions 1.2 x 0.8 x 1.6 m and the inner dimensions 1.19 x 0.79 x 1.59 m. the boxes are loaded on a vehicle (truck + trailer). the available capacity in the vehicle combination is 140 m3. each valve has a volume of 0.06 m3. - calculate the load factor on the box level (%). - calculate the load factor on the vehicle level (%). - calculate the overall load factor (%).

Finally, the arena decides to offer advertising space on the jerseys of the arena’s own amateur volley ball team. the arena wants the probability of being shortlisted to be 0.14. what is this as a percentage and a fraction? what is the probability of not being shortlisted? give your answer as a decimal. those shortlisted are entered into a final game of chance. there are six balls in a bag (2 blue balls, 2 green balls and 2 golden balls). to win, a company needs to take out two golden balls. the first ball is not replaced. what is the probability of any company winning advertising space on their volley ball team jerseys?

The graph of y=x3 is transformed as shown in the graph below. which equation represents the transformed function?