If sin (π/2 +x) = cos x cos (π/2 + x) = -sin x tan (π/2 + x) = -cot x cot (π/2 + x)  = -tan x sec (π/2 + x) = ? cosec (π/2 + x) = ?  This is a question from Trigonometric functions and is...

If

sin (π/2 +x) = cos x

cos (π/2 + x) = -sin x

tan (π/2 + x) = -cot x

cot (π/2 + x)  = -tan x

sec (π/2 + x) = ?

cosec (π/2 + x) = ?

 

This is a question from Trigonometric functions and is related to deriving the formulae.

Asked on by alpine-c5

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beckden | High School Teacher | (Level 1) Educator

Posted on

Since `sec(x) = 1/(cos(x))` and `csc(x) = 1/(sin(x))`

`sec(pi/2 + x) = 1/(cos(pi/2 + x)) = 1/(-sin(x)) = -1/(sin(x)) = -csc(x)`

`csc(pi/2 + x) = 1/(sin(pi/2 + x)) = 1/(cos(x)) = sec(x)`

so

`sec(pi/2 + x) = -csc(x)`
`csc(pi/2 + x) = sec(x)`

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