How do you prove cscx = sec(pi/2 - x)?

2 Answers
Mar 29, 2018

Since this is an identity,

the relation is true for all values of x

Explanation:

Given:

cscx=sec(pi/2-x)

cscx=1/sinx

sec(pi/2-x)=1/cos(pi/2-x)

Thus,

1/sinx=1/cos(pi/2-x)

cos(pi/2-x)=sinx

Since this is an identity,

the relation is true for all values of x

Mar 29, 2018

See below

Explanation:

Using:
secx=1/cosx
1/sinx=cscx
cos(x-y)=cosxcosy+sinxsiny

Start:
cscx=sec(pi/2-x)

cscx=1/cos(pi/2-x)

cscx=1/(cos(pi/2)cosx+sin(pi/2)*sinx)

cscx=1/(cancel(0*cosx)+1*sinx)

cscx=1/sinx

cscx=cscx