IF A=30 DEGREE; SHOW THAT-
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Heya friend here is your answer
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A = 30°
LHS = (sin A - cos A)²
= (sin 30° - cos 30°)²
= (½ - √3/2)²
= {(1-√3)/2}²
= 1²+√3²-2(1)(√3)/4
= 1+3-2√3/4
= (4-2√3)/4
= 2(2-√3)/2(2)
= (2-√3)/2
RHS = 1 - sin 2A
= 1 - sin 2(30°)
= 1- sin 60°
= 1-√3/2
= (2-√3)/2
Therefore, LHS = RHS
So, (sin A - cos A)² = 1 - sin 2A for which A = 30°
LHS = (sin A - cos A)²
= (sin 30° - cos 30°)²
= (½ - √3/2)²
= {(1-√3)/2}²
= 1²+√3²-2(1)(√3)/4
= 1+3-2√3/4
= (4-2√3)/4
= 2(2-√3)/2(2)
= (2-√3)/2
RHS = 1 - sin 2A
= 1 - sin 2(30°)
= 1- sin 60°
= 1-√3/2
= (2-√3)/2
Therefore, LHS = RHS
So, (sin A - cos A)² = 1 - sin 2A for which A = 30°
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