Question

If A = 30°;
show that:
(sinA - cosA)² = 1 - sin2A

Answer 1

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