Find a numerical value of one trigonometric function of x for cscx = sinx tanx + cosx

Mathematics

1 answer:

Alex787 [66]3 years ago

6 0

Answer:

Step-by-step explanation:

we have

$cscx = sinx tanx + cosx\\\\\frac{1}{sinx}=sinx.\frac{sinx}{cosx} +cosx\\\\\frac{1}{sinx}.sinx.cosx= sinx.\frac{sinx}{cosx}.sinx.cosx+cosx.sinx.cosx\\ cosx= (sinx)^{3} +sinx.(cosx)^{2} \\cosx= sinx[(sinx)^{2}+(cosx)^{2})\\ cosx=sinx.1\\cosx=sinx\\tanx=1\\x=\frac{\pi}{4} +k\pi,k-integer.$

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If and CX = 5 units, what is DZ?

NeTakaya

The question is missing the figure. So, it is attached below.

Answer:

DZ = 4 units

Step-by-step explanation:

Given:

CD || XZ

YC = 25 units, CX = 5 units, YD = 20 units.

We know that,

If CD is parallel to XZ , then the line CD divides the sides XY and YZ of the triangle XYZ proportionally. This is true by triangle proportionality theorem.

Therefore, the lengths YC, CX, YD and DZ are in proportion. This gives,

$\frac{YC}{CX}=\frac{YD}{DZ}$