Question

Please help me solve this

Answer 1

See below

Step by step explanation

`\tan( (\pi)/(4) + </strong><strong>A</strong><strong>) \tan( (3\pi)/(4) + </strong><strong>A</strong><strong>) </strong><strong>=</strong><strong> </strong><strong>-</strong><strong> </strong><strong>1</strong><strong> </strong><strong>`

L.H.S

`\tan( (\pi)/(4) + </strong><strong>A</strong><strong>) \tan( (3\pi)/(4) + </strong><strong>A</strong><strong> )`

We know that ,

(tan π / 4 = 1 )

[ tan ( π - B ) = - tan∅ ]

`( (1 + tan \: </strong><strong>A</strong><strong>)/(1 - tan \: </strong><strong>B</strong><strong>) )( ( - 1 + \tan\: </strong><strong>A</strong><strong> )/(1 + \tan \: </strong><strong>A</strong><strong> ) )`

`= ( - (1 - \tan\: </strong><strong>A</strong><strong>))/((1 - \tan \: </strong><strong>A</strong><strong>) )`

`= - 1`

L.H.S = R.H.S

Proved

Hope this helps..

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