Question

If 2 cos (x + y) = 1, and 2 sin (x - y) = 1, find the
values of x and y.
​

Answer 1

Step-by-step explanation:

2 cos (x + y) = 1, and 2 sin (x - y) = 1

2 ( cosxcosy-sinxsiny) = 1

2 ( sinxcosy-cosxsiny) = 1

Apply this formula and solve

Answer 2

★ Solution :- ★

Given , that

• 2cos(x + y) = 1

Simplifying

➵ cos(x + y) = 1/2

As we know that cos60° = 1/2 . By comparing with cos(x + y)

➵ x + y = 60°

Assuming as equation 1

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And given that

• 2sin(x - y) = 1

Simplifying

➠ sin(x - y) = 1/2

As we know that sin30° = 1/2 . By comparing we th sin(x - y)

➠ x - y = 30°

Assuming as equation 2

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Now , equation (1 + 2)

➸ x + y + (x - y) = 60° + 30°

➸ x + y + x - y = 90°

➸ 2x = 90°

➸ x = 90° ÷ 2

➸ x = 45°

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Now, finding y by substituting the value of x in equation 1

➻ x + y = 60°

➻ 45° + y = 60°

➻ y = 60° - 45°

➻ y = 15°

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Hence ,

• x = 45°
• y = 15°