If x + y = 90, simplify (sinx + siny)2−2sinxsiny

Question 1 Report

-1

Answer Details

x + y = 90

Solve for

(\sin x + \sin y)^{2} - 2 \sin x \sin y

x + y = 90

---(1)

(\sin x + \sin y)^{2} - 2 \sin x \sin y

----(2)

x = 90 - y

---(3)
Expanding eqn (2)
Therefore:

\sin^{2} x + \sin^{2} y + 2 \sin x \sin y - 2 \sin x \sin y

\sin^{2} x + \sin^{2} y

--- (4)
Substitute the value of

x

in eqn (3) into eqn (4)
=>

\sin^{2} (90 - y) + \sin^{2} y

---(5)
Expanding eqn (5)
=>

\sin^{2} (90) - \sin^{2} y + \sin^{2} y

\sin^{2} (90) + 0

\sin^{2} (90)

(\sin (90))^{2}

1^{2}

1

Explanation provided by Nate Falasinu

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