Is sin(t)csc(pi/2-t)=tan(t) ?

The answer to whether sin(t)csc(pi/2-t)=tan(t) is True

Popular >

prove sin(t)csc(pi/2-t)=tan(t)

prove

sin (t) csc (\frac{π}{2} - t) = tan (t)

True

Solution steps

sin (t) csc (\frac{π}{2} - t) = tan (t)

Manipulating left side

sin (t) csc (\frac{π}{2} - t)

Rewrite using trig identities

= sin (t) \frac{1}{cos ( t )}

Simplify

sin (t) \frac{1}{cos ( t )} : \frac{sin ( t )}{cos ( t )}

= \frac{sin ( t )}{cos ( t )}

Use the basic trigonometric identity:

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

= tan (t)

We showed that the two sides could take the same form

\Rightarrow True

cos (x) cot (x) = csc (x) - sin (x)

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

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

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

\frac{1}{tan ( β )} + tan (β) = sec (β) csc (β)

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