How many t does inverse sine equal inverse cosine?

Question

How many t does sin^–1 t = cos^–1 t?

1.) 0

2.) 1

3.) 2

4.) 3

5.) Infinitely many

Answer 1

one time at sqrt(2)/2

Answer 2

updated

I almost concur with Billy's answer.

but thinking more, there are two values

t=√2/2 and t= -√2/2

t must be between -1 and 1

the angles generated by the inverses are multi-valued

cos^-1t=sin^-1t,,,,,,,angle=angle

same as

sin^-1√(1-t²)=sin^-1t,,,,,,,angle=angle

take sin both sides of equation provides value=value

√(1-t²)=t

2t²=1

t=+/-√2/2

at the plus value, cos^-1 and sin^-1 are pi/4 +2kpi where t solves equation

or 7pi/4+2kpi for cos^-1 and 3pi/4+2kpi for sin^-1 which are not solution points

at the minus value cos^-1 and sin^-1=5pi/4+2kpi, which are solution points

and cos^-1=3pi/4+2kpi and sin^-1=7pi/4+2pik which are not solution points.

If you plot y1=sin^-1x and y2=cos^-1x

they intersect at x=+√2/2 and x= -√2/2