Answer:
A. Use the complementary relationship between sine and cosine to rewrite sin(x + y) as Cosine (StartFraction pi over 2 EndFraction minus (x + y) ). Apply the cosine sum identity. Then simplify using sin(–y) = –sin(y) and cos(–y) = cos(y).
Step-by-step explanation:
edge
The supplementary relationship between sine and cosine
to write sin(x + y) is sin x cos y + cos x sin y. and correct steps are
Use the complementary relationship between sine and cosine to rewrite sin(x + y) as Cosine (Start Fraction pi over 2 End Fraction minus (x + y) ). Apply the cosine sum identity. Then simplify using sin(–y) = –sin(y) and cos(–y) = cos(y).
Trigonometric equation is an equation involving one or more trigonometric ratios of unknown angles. It is expressed as ratios of sine(sin), cosine(cos), tangent(tan), cotangent(cot), secant(sec), cosecant(cosec) angles. For example, cos2 x + 5 sin x = 0 is a trigonometric equation.
What is Sin(a + b) Identity in Trigonometry?
Sin(a + b) is the trigonometry identity for compound angles. It is applied when the angle for which the value of the sine function is to be calculated is given in the form of the sum of angles. The angle (a + b) represents the compound angle.
sin (a + b) = sin a cos b + cos a sin b
According to the question
sin(x+y)
= cos ([tex]\frac{\pi }{2} - (x+y)[/tex])
Now as (cos (x-y) = cosx cosy - sinx siny )
= Cos ([tex]\frac{\pi }{2}-x[/tex])cos(-y) - sin([tex]\frac{\pi }{2}-x[/tex])sin(-y)
By using identity sin(–y) = –sin(y) and cos(–y) = cos(y)
= Cos ([tex]\frac{\pi }{2}-x[/tex])cos(-y) - sin([tex]\frac{\pi }{2}-x[/tex])sin(-y)
= sin x cos y - cos x sin(-y)
= sin x cos y + cos x sin y
Hence, the supplementary relationship between sine and cosine
to write sin(x + y) is sin x cos y + cos x sin y. and correct steps are
Use the complementary relationship between sine and cosine to rewrite sin(x + y) as Cosine (Start Fraction pi over 2 End Fraction minus (x + y) ). Apply the cosine sum identity. Then simplify using sin(–y) = –sin(y) and cos(–y) = cos(y).
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