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

User Splines
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1 Answer

6 votes

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

User Evan Broder
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