English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

الحلّ

prove

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

صحيح

خطوات الحلّ

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

قم بالعمل على الطرف الأيمن

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

Rewrite using trig identities

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

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

:فعّل نطريّة فيتاغوروس

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

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

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

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

وسٌع:

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

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

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

a (b - c) = ab - a c

: افتح أقواس بالاستعانة بـ

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

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

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

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

اضرب

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

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

Rewrite using trig identities

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

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

:Use the basic trigonometric identity

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

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

بسّط:

sin^{2} (y)

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

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

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

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

:فعّل قانون القوى

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

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

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

:اضرب كسور

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

cos^{2} (y) :

إلغ العوامل المشتركة

= sin^{2} (y)

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

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

أظهرنا بأنّ الطرفين من الممكن أن تكون لهما نفس الصورة

\Rightarrow صحيح

p ro v e sin (θ) (1 + cot^{2} (θ)) = csc (θ)

p ro v e 5 + cot^{2} (x) = 4 + csc^{2} (x)

p ro v e sin^{2} (2 x) = \frac{1 - cos ( 4 x )}{2}

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

p ro v e sin^{2} (θ) sec^{2} (θ) csc^{2} (θ) = sec^{2} (θ)