Question

Prove the following identity


sin x(sec x+cscx)= tan x +1

Answer 1

Explanation:

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FACTS TO KNOW BEFORE SOLVING :-

• 
  `\sin x = (1)/(cosec \: x) \: \: or \: \: cosex \: x = (1)/(\sin x)`

• 
  `\cos x = (1)/(\sec x) \: \:or \: \: \sec x = (1)/(\cos x)`

• 
  `\tan x = (\sin x)/(\cos x)`

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In the question ,

L.H.S. =
`\sin x (\sec x + cosec \: x)`

R.H.S. =
`\tan x + 1`

Lets solve L.H.S. first.

`\sin x (\sec x + cosec \: x)`

`=> \sin x( (1)/(\cos x) + (1)/(\sin x) )`

`=> (\sin x)/(\cos x) + (\sin x)/(\sin x)`

`=> \tan x + 1`

∴ L.H.S. = R.H.S. (Proved)