Find one solution for each equation. Assume all angles involved a...

Question

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3.

csc(β + 40°) = sec(β - 20°)

Accepted Answer

Welcome back. I am so glad you're here. We're asked to solve the following trigonometric equation. Consider all the angles as acute angles. We're told that the Koi Can't of alpha plus 75 degrees is equal to the C can't of alpha minus 35 degrees. Our answer choices are answer choice. A 50 degrees. Answer choice. B 25 degrees. Answer choice, C 55 degrees and answer choice. D 52 degrees. All right. Well, cos can't and C can't are co functions. So this statement is true. If the sum of these angles are CC cans, alpha plus 75 and C cans alpha minus 35 is 90 degrees. So we can add these up, set it equal to 90 degrees and solve for alpha. So we take our Koi cans alpha plus 75 degrees plus our C cans angle, alpha minus 35 degrees. Set that equal to 90 degrees. Now we can combine like terms. So our alpha plus our alpha is going to give us two alpha and then our positive 75 degrees minus 35 degrees will give us plus 40 degrees equals 90 degrees. We can subtract the 40 degrees from both sides. And we have two alpha equals 50 degrees. And now dividing both sides by two, we have solved for alpha, alpha is equal to 50 degrees, divided by two is 25 degrees. And there's our solution, we look at our answer choices and this matches with answer choice. B well done. We'll catch you on the next one.

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Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. csc(β + 40°) = sec(β - 20°)