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פּוֹפּוּלָרִי >

prove 0=cot(x)sin(x)-cos^2(x)sec(x)

פתרון

prove

0 = cot (x) sin (x) - cos^{2} (x) sec (x)

פתרון

נכון

צעדי פתרון

0 = cot (x) sin (x) - cos^{2} (x) sec (x)

עבוד על אגף ימין

cot (x) sin (x) - cos^{2} (x) sec (x)

sin, cos :

בטא באמצאות

- cos^{2} (x) sec (x) + cot (x) sin (x)

sec (x) = \frac{1}{cos ( x )}

:Use the basic trigonometric identity

= - cos^{2} (x) \frac{1}{cos ( x )} + cot (x) sin (x)

cot (x) = \frac{cos ( x )}{sin ( x )}

:Use the basic trigonometric identity

= - cos^{2} (x) \frac{1}{cos ( x )} + \frac{cos ( x )}{sin ( x )} sin (x)

- cos^{2} (x) \frac{1}{cos ( x )} + \frac{cos ( x )}{sin ( x )} sin (x) = 0

- cos^{2} (x) \frac{1}{cos ( x )} + \frac{cos ( x )}{sin ( x )} sin (x)

cos^{2} (x) \frac{1}{cos ( x )} = cos (x)

cos^{2} (x) \frac{1}{cos ( x )}

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

:הכפל שברים

= \frac{1 \cdot cos ^{2} ( x )}{cos ( x )}

1 \cdot cos^{2} (x) = cos^{2} (x) :

הכפל

= \frac{cos ^{2} ( x )}{cos ( x )}

cos (x) :

בטל את הגורמים המשותפים

= cos (x)

\frac{cos ( x )}{sin ( x )} sin (x) = cos (x)

\frac{cos ( x )}{sin ( x )} sin (x)

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

:הכפל שברים

= \frac{cos ( x ) sin ( x )}{sin ( x )}

sin (x) :

בטל את הגורמים המשותפים

= cos (x)

= - cos (x) + cos (x)

- cos (x) + cos (x) = 0 :

חבר איברים דומים

= 0

= 0

= 0

הראנו ששני האגפים יכולים להיות מאותה הצורה

\Rightarrow נכון

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