Solve: Sin(45)xCos(45)xTan(45).
The above is given in degrees.
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Approach 1: We know that,
sin 4 5 o = cos 4 5 o = 2 1
and, tan 4 5 o = 1
So, sin 4 5 o × cos 4 5 o × tan 4 5 o = ( 2 1 × 2 1 × 1 )
⇒ sin 4 5 o × cos 4 5 o × tan 4 5 o = 2 × 2 1 = 2 1 = 0 . 5
Approach 2:
sin A × cos A × tan A = sin A × cos A × cos A sin A
Cancelling cos A with the c o s A in the denominator,
⇒ sin A × cos A × tan A = ( sin A ) 2
Here A = 4 5 o , so,
⇒ sin A × cos A × tan A = ( 2 1 ) 2 = 2 1 = 0 . 5