Is (1+tan^2(x))/(cot^2(x)+1)=tan^2(x) ?

The answer to whether (1+tan^2(x))/(cot^2(x)+1)=tan^2(x) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove (1+tan^2(x))/(cot^2(x)+1)=tan^2(x)

prove

\frac{1 + tan ^{2} ( x )}{cot ^{2} ( x ) + 1} = tan^{2} (x)

True

Solution steps

\frac{1 + tan ^{2} ( x )}{cot ^{2} ( x ) + 1} = tan^{2} (x)

Manipulating left side

\frac{1 + tan ^{2} ( x )}{cot ^{2} ( x ) + 1}

Express with sin, cos

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

Rewrite using trig identities

tan^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

7 sec (y) cos (y) = 7

(1 + sin (a)) (1 - sin (a)) = \frac{1}{sec ^{2} ( a )}

sec (a) (1 - sin^{2} (a)) = cos (a)

cos (x + y) - cos (x - y) = - 2 sin (x) sin (y)

sec (\frac{π}{2} - u) = csc (u)

Is (1+tan^2(x))/(cot^2(x)+1)=tan^2(x) ?
The answer to whether (1+tan^2(x))/(cot^2(x)+1)=tan^2(x) is True