Is sec(pi/2-y)=csc(y) ?

The answer to whether sec(pi/2-y)=csc(y) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove sec(pi/2-y)=csc(y)

prove

sec (\frac{π}{2} - y) = csc (y)

True

Solution steps

sec (\frac{π}{2} - y) = csc (y)

Manipulating left side

sec (\frac{π}{2} - y)

Rewrite using trig identities

= \frac{1}{sin ( y )}

Rewrite using trig identities

csc (y)

We showed that the two sides could take the same form

\Rightarrow True

cos (2 x - \frac{π}{2}) = cos (\frac{π}{2} - 2 x)

sin (\frac{π}{2} - x) cot (\frac{π}{2} + x) = - sin (x)

cos (x) \cdot csc (x) \cdot tan (x) = 1

- 2 sin (2 (x + 45)) = 2 cos (2 x)

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