(Angle AEB = 2x = angle ABC, Angle ABE = angle ACB = x)

therefore,

AB/AE=BC/EB = AC/AB

so, AB/AE = BC/EC (given EB=EC)

AB =BC.AE/EC ...(1)

By intercept theorem:

DM/MC = AE/EC ...(2)

subst (2) in (1):

AB = BC.DM/MC

DM = AB.MC/BC = AB/2

cheers.

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Using the SATC quadrants, we have for cos^{−1} (6/17):

and for cos^{−1} (−6/17)

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So you have the `R`-formula

And from the notes above, the maximum/minimum value of a `R`-formula is ±`R` so

At this juncture, there'll be a insatiable urge to flip the centre term and make the careless mistake of flipping the inequality signs, +20 on both sides to get what you want i.e.

(✘)

Not only does the above don't make any mathematical sense (3 ≥ `x` ≥ 37!), one has to always consider the *nature of the graph* you're dealing with when it comes to inequalities. From your Trigonometric Equations & Graphs, you know that the max/min values of a `A` cos `x` curve is still ±`A`, even when you flip it around for −`A` cos `θ`, as shown:

So you may now 安安心心 proceed in a as follows:

∴ Maximum value of **37** occurs when

and minimum value of **3** occurs when

Note: `x` = −1.08 rejected ∵ 0 ≤ `x` ≤ 2`π`

8 cos x - 15 sin x = 17 cos (x + 1.08) -------- (R formula)

1. Find the minimum and maximum value of 20 - 8 cos x + 15 sin x and the corresponding x values for 0 ≤ x ≤ 2π.

2. Solve the equation |8 cos x - 15 sin x| = 6 for 0 ≤ x ≤ 2π.

Thanks in advance!

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