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प्रश्न
If A = 30°;
show that:
(sinA - cosA)2 = 1 - sin2A
उत्तर
Given that A = 30°
LHS = `(sin "A" – cos "A")^2`
=`(sin 30° – cos 30°)^2`
=`((1)/(2) – (sqrt3)/(2))^2`
= `(1)/(4) + (3)/(4) – (sqrt3)/(2)`
= `1 – (sqrt3)/(2)`
= `2 – (sqrt3)/(2)`
RHS = 1 – sin 2A
= 1 – sin 2(30°)
= 1 – sin60°
= `1 – (sqrt3)/(2)`
= `(2 – sqrt3)/(2)`
LHS = RHS
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