Math  /  Trigonometry

Question12) XYZX Y Z is a right-angled triangle at YY, if YZ=2XYY Z=2 X Y Find the value of each of :tanZ,tanX,cosZ,cos: \tan Z, \tan X, \cos Z, \cos

Studdy Solution
Calculate cosX\cos X. By definition:
cosX=adjacenthypotenuse=YZXZ \cos X = \frac{adjacent}{hypotenuse} = \frac{YZ}{XZ}
Substitute the known lengths:
cosX=2aa5=25=255 \cos X = \frac{2a}{a\sqrt{5}} = \frac{2}{\sqrt{5}} = \frac{2\sqrt{5}}{5}
Solution: tanZ=12 \tan Z = \frac{1}{2} tanX=2 \tan X = 2 cosZ=55 \cos Z = \frac{\sqrt{5}}{5} cosX=255 \cos X = \frac{2\sqrt{5}}{5}

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