Is tan(pi/2-x)sec(x)=csc(x) ?

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

Popular >

prove tan(pi/2-x)sec(x)=csc(x)

prove

tan (\frac{π}{2} - x) sec (x) = csc (x)

True

Solution steps

tan (\frac{π}{2} - x) sec (x) = csc (x)

Manipulating left side

tan (\frac{π}{2} - x) sec (x)

Rewrite using trig identities

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

Multiply fractions:

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

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

Express with sin, cos

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

Rewrite using trig identities

csc (x)

We showed that the two sides could take the same form

\Rightarrow True

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

sec (u) cos (u) - sin^{2} (u) = cos^{2} (u)

\frac{tan ^{2} ( x )}{sec ( x )} + cos (x) = sec (x)

tan^{2} (x) cot^{2} (x) = 1

cos (π + θ) = - cos (θ)

Is tan(pi/2-x)sec(x)=csc(x) ?
The answer to whether tan(pi/2-x)sec(x)=csc(x) is True