English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

פּוֹפּוּלָרִי >

prove tan^2(B)-sin^2(B)=tan^2(B)sin^2(B)

פתרון

prove

tan^{2} (B) - sin^{2} (B) = tan^{2} (B) sin^{2} (B)

נכון

צעדי פתרון

tan^{2} (B) - sin^{2} (B) = tan^{2} (B) sin^{2} (B)

עבוד על אגף ימין

tan^{2} (B) sin^{2} (B)

Rewrite using trig identities

tan^{2} (B) sin^{2} (B)

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

:הפעל זהות פיטגורית

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

= tan^{2} (B) (1 - cos^{2} (B))

= tan^{2} (B) (1 - cos^{2} (B))

(1 - cos^{2} (B)) tan^{2} (B)

הרחב את:

tan^{2} (B) - tan^{2} (B) cos^{2} (B)

(1 - cos^{2} (B)) tan^{2} (B)

= tan^{2} (B) (1 - cos^{2} (B))

a (b - c) = ab - a c

: פתח סוגריים בעזרת

a = tan^{2} (B), b = 1, c = cos^{2} (B)

= tan^{2} (B) \cdot 1 - tan^{2} (B) cos^{2} (B)

= 1 \cdot tan^{2} (B) - tan^{2} (B) cos^{2} (B)

1 \cdot tan^{2} (B) = tan^{2} (B) :

הכפל

= tan^{2} (B) - tan^{2} (B) cos^{2} (B)

= tan^{2} (B) - cos^{2} (B) tan^{2} (B)

Rewrite using trig identities

tan^{2} (B) - cos^{2} (B) tan^{2} (B)

tan (B) = \frac{sin ( B )}{cos ( B )}

:Use the basic trigonometric identity

= tan^{2} (B) - cos^{2} (B) (\frac{sin ( B )}{cos ( B )})^{2}

cos^{2} (B) (\frac{sin ( B )}{cos ( B )})^{2}

פשט את:

sin^{2} (B)

cos^{2} (B) (\frac{sin ( B )}{cos ( B )})^{2}

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

(\frac{sin ( B )}{cos ( B )})^{2}

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

:הפעל את חוק החזקות

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

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

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

:הכפל שברים

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

cos^{2} (B) :

בטל את הגורמים המשותפים

= sin^{2} (B)

= tan^{2} (B) - sin^{2} (B)

= tan^{2} (B) - sin^{2} (B)

הראנו ששני האגפים יכולים להיות מאותה הצורה

\Rightarrow נכון

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

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

- tan (t) - \frac{cos ( t )}{sin ( t ) - 1} = sec (x)

\frac{cot ( x )}{tan ( x ) sec ( x )} = csc (x) - 1

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