are 12. Suppose that 6 is an acute angle in a right triangle and ion 2p²q² sin 0= p + Find cos 0 and tan 0. q* 13. This problem is adapted from the text An Elementary Treatise on Plane Trigonometry, by R. D. Beasley, first published in 1884. (a) Prove the following identity, which will be used in part (b): 1 + tan? a = sec2 a. (b) Suppose that a and 0 are acute angles and 1 + tan a tan 0 Express sin 0 and cos 0 in 1-tan a terms of a. Hint: Draw a right triangle, label one of the angles 0, and let the lengths of the sides opposite and ad- jacent to 0 be 1 + tan a and 1- tan a, respectively. 20 Answer: sin 0 = (cos a + sin a)/V2 cos e = (cos a – sin a)/V2 (A200 cos 14. If 0 = T/4, evaluate each of the following. Exact answers are required, not calculator approximations. %3D (d) cos 30 (e) cos(20/3) (f) (cos 30)/3 (a) cos 0 (g) cos(-0) (h) cos (50) (b) cos³ 0 (c) cos 20 In Exercises 15–22, convert each expression into one involving only sines and cosines and then simplify. (Leave your answers in terms of sines and/or cosines.) sin A + cos A 15. sec A + csc A csc A sec A 16. sec² A + csc² A sin A sec A 18. cos A + tan A sin A 17. tan A + cot A sin A +. 1-cot A cos A 19. 1- tan A 20. sec A - 1 sec A + 1

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.