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junior college 1 | H2 Maths
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how is it simplified to -sin(π/2-2x)?
Date Posted: 3 years ago
Views: 414
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Simple. Recall the double angle formula for sine :
sin 2A = 2 sin A cos A
Here, your A = π/4 - x and 2A = 2(π/4 - x) = π/2 - 2x
So,
2［sin (π/4 - x)］［cos (π/4 - x)］(-1)
= -2［sin (π/4 - x)］［cos (π/4 - x)］
= -sin(2(π/4 - x))
= -sin(π/2 - 2x)
sin 2A = 2 sin A cos A
Here, your A = π/4 - x and 2A = 2(π/4 - x) = π/2 - 2x
So,
2［sin (π/4 - x)］［cos (π/4 - x)］(-1)
= -2［sin (π/4 - x)］［cos (π/4 - x)］
= -sin(2(π/4 - x))
= -sin(π/2 - 2x)
thank u!!
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