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π/4 -x/2
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your answer is in the attachment.
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Heya
_______________________________
Cos x = Cos²x/2 - Sin² x/2
And
( 1 - Sinx ) = ( Cosx/2 - Sinx/2 )²
=>
Tan-¹ { Cos²x/2 - Sin²x/2} / (Cosx/2-Sinx/2)²
=>
Tan-¹ { Tan ( π/4 + x/2 ) }
=>
π/4 + x/2
_______________________________
Cos x = Cos²x/2 - Sin² x/2
And
( 1 - Sinx ) = ( Cosx/2 - Sinx/2 )²
=>
Tan-¹ { Cos²x/2 - Sin²x/2} / (Cosx/2-Sinx/2)²
=>
Tan-¹ { Tan ( π/4 + x/2 ) }
=>
π/4 + x/2
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