Question

if sin A = √3/2 find the value of 2 cot²A -1

Answer 1

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Given , sinA = √3 / 2

To find the value of : 2 cot²A - 1 ----- ( i )

Now ,

cosA = √ ( 1 - sin²A )

[ • sin²A + cos²A = 1 → Using this identity ]

cosA = √ { 1 - ( √3 / 2 )² } [ • Putting the value of sinA ]

cosA = √ ( 1 - 3 / 4 )

cosA = √ { ( 4 - 3 ) / 4 }

cosA = √ ( 1 / 4 )

cosA = 1 / 2

We know ,

cotA = cosA / sinA

cotA = ( 1 / 2 ) / ( √3 / 2 ) [ • Putting the values of sinA and cosA ]

cotA = ( 1 / 2 ) × ( 2 / √3 )

cotA = 1 / √3

Now putting the value of cotA in equation--( i )

• 2 cot²A - 1

= 2 × ( 1 / √3 )² - 1

= 2 × 1 / 3 - 1

= ( 2 / 3 ) - 1

= ( 2 - 3 ) / 3

= - 1 / 3 [ ★ Required answer ]

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$<b><u><marquee direction> Hope it helps !!$