Question

solve :-
Sin[arc cos1by2]
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Answer 1

Heya!!

Sin ( Cos-¹ 1/2 ) = ?

Put Cos-¹ (1/2) = x we have

Sin ( x ) = ? ... ( i )

1/2 = Cos ( x )

Sin² x + Cos² x = 1

Sin² x = 1 - Cos² x

Sin x = √(1 -1/4 )

x = Sin-¹ (√3/2 )

Now, put value of x in i we have

Sin ( Sin-¹ √3/2 )

= √3/2