Question

If x cos 60° + y cos 0° + sin 30° −  cot 45° = 5, then find the value of x + 2y.

Answer 1

Given:

x cos 60° + y cos 0° + sin 30° − cot 45° = 5

Trigonometric Values

cos 60° = `1/2`

cos 0° = 1

sin 30° = `1/2`

cot 45° = 1

Substituting these values in the given equation:

`x xx 1/2 + y xx 1 + 1/2 - 1 = 5`

Simplify the Equation

⇒ `x/2 + y - 1/2 = 5`

⇒ `x/2 + y - 1/2 = 5`

⇒ `x/2 + y = 5 + 1/2`

⇒ `x/2 + y = 10/2 + 1/2`

⇒ `x/2 + y = 11/2`      ...(Multiply the entire equation by 2)

⇒ `2 xx x/2 + 2 xx y = 2 xx 11/2` 

⇒ x + 2y = 11

Thus, the final answer is 11.