Question

Cot(x) + tan(x) = sec(x) csc(x) for all real numbers x ≠ ???? 2 n for integer n.

Answer 1

To prove:
`\cot x+\tan x=\sec x\csc x`

where
`x\\eq (\pi)/(2)(2n-1)`

Using trigonometry formula:

`\cot x=(\cos x)/(\sin x)`

`\tan x=(\sin x)/(\cos x)`

`\sec x=(1)/(\cos x)`

`\csc x=(1)/(\sin x)`

Taking Left hand side

`\Rightarrow (\cos x)/(\sin x)+(\sin x)/(\cos x)`

`\Rightarrow (\cos^2 x+\sin^2x)/(\sin x\cos x)`

`\Rightarrow (1)/(\sin x\cos x)`
`\because \cos^2 x+\sin^2x=1`

`\Rightarrow \sec x\csc x`

Hence proved