Question

If cosA+cos(square)A=1 prove that sin(square)A+sin(to th
e power 4) =1

Answer 1

$<b><font face=Copper black size=4 colour=purple>$
$<b><marquee direction = "up" > <h3>$Given :

cos A + cos²A = 1 __________( 1 )

cos A = 1 - cos²A

{ Using identity -

sin²A + cos²A = 1

•°• sin²A = 1 - cos²A }

cos A = sin²A _________ ( 2 )

Squaring both sides of ( 2 )

( cos A )² = ( sin²A )²

cos²A = sin⁴A ___________( 3 )

Now,

sin²A + sin⁴A -

= cos A + cos²A [ Using ( 2 ) and ( 3 ) ]

= 1 [ Using ( 1 ) ]

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