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JAMB Mathematics 2015 Paper

Question : 9

Total: 61

(\sin x + \sin y)^2

−2sinxsiny

Solution:

Concept:

Use the complementary angle identity and the Pythagorean identity to simplify the trigonometric expression.

Explanation:

Start by expanding the square:

(\sin x + \sin y)^2 = \sin^2 x + 2\sin x \sin y + \sin^2 y

Subtract

2\sin x \sin y

from both sides:

(\sin x + \sin y)^2 - 2\sin x \sin y = \sin^2 x + \sin^2 y

Given

x + y = 90^{\circ}

, we have

y = 90^{\circ} - x

Using the complementary angle identity,

\sin(90^{\circ} - x) = \cos x

Thus,

\sin y = \cos x

Substitute into the expression:

\sin^2 x + \sin^2 y = \sin^2 x + \cos^2 x

By the Pythagorean identity,

\sin^2 x + \cos^2 x = 1

Therefore, the simplified value is

1

Answer:

1

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