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prove cos^2(x)csc(x)sec(x)=cot(x)

פתרון

prove

cos^{2} (x) csc (x) sec (x) = cot (x)

נכון

צעדי פתרון

cos^{2} (x) csc (x) sec (x) = cot (x)

עבוד על אגף שמאל

cos^{2} (x) csc (x) sec (x)

sin, cos :

בטא באמצאות

cos^{2} (x) csc (x) sec (x)

csc (x) = \frac{1}{sin ( x )}

:Use the basic trigonometric identity

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

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

:Use the basic trigonometric identity

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

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

פשט את:

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

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

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

:הכפל שברים

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

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

הכפל

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

cos (x) :

בטל את הגורמים המשותפים

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

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

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

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

:Use the basic trigonometric identity

= cot (x)

הראנו ששני האגפים יכולים להיות מאותה הצורה

\Rightarrow נכון

p ro v e \frac{cos ^{2} ( - x ) csc ( x )}{cot ( x )} = cos (x)

p ro v e cot (2 x) = \frac{csc ^{2} ( x ) - 2}{2 cot ( x )}

p ro v e \frac{1}{cos ( θ )} = \frac{tan ( θ )}{sin ( θ )}

p ro v e sin (x) \cdot tan (x) = sec (x) - cos (x)

p ro v e (tan (y) + cot (y)) sin (y) cos (y) = 1