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Verizon [17]
3 years ago
5

Use the fundamental identities and appropriate algebraic operations to simplify the following expression. (18 +tan x) (18-tan x)

+ sec 2x Complete the following statement The lowest point on the graph of y = cos x, 0sxs2x, occurs when x-

Mathematics
1 answer:
andrezito [222]3 years ago
3 0

Answer:

a) \left(18+\tan \left(x\right)\right)\left(18-\tan \left(x\right)\right)+\sec ^2\left(x\right)=325

b) The lowest point of y=\cos \left(x\right), 0\leq x\leq 2\pi is when x = \pi

Step-by-step explanation:

a) To simplify the expression \left(18+\tan \left(x\right)\right)\left(18-\tan \left(x\right)\right)+\sec ^2\left(x\right) you must:

Apply Difference of Two Squares Formula: \left(a+b\right)\left(a-b\right)=a^2-b^2

a=18,\:b=\tan \left(x\right)

\left(18+\tan \left(x\right)\right)\left(18-\tan \left(x\right)\right)=18^2-\tan ^2\left(x\right)=324-\tan ^2\left(x\right)

324-\tan ^2\left(x\right)+\sec ^2\left(x\right)

Apply the Pythagorean Identity 1+\tan ^2\left(x\right)=\sec ^2\left(x\right)

From the Pythagorean Identity, we know that 1=-\tan ^2\left(x\right)+\sec ^2\left(x\right)

Therefore,

324[-\tan ^2\left(x\right)+\sec ^2\left(x\right))]\\324[+1]\\325

b) According with the below graph, the lowest point of y=\cos \left(x\right), 0\leq x\leq 2\pi is when x = \pi

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