Answer: 15
Step-by-step explanation:
Recall : if sin α = cos β , then α + β are complementary , that is
α + β = 90
Since sin (2x+7) = cos(4x-7) , then (2x+7) and (4x-7) are complementary , that is:
2x + 7 + 4x - 7 = 90
6x = 90
x = 90/6
x = 15
The missing value x is constituting the angles of both sin and cos trigonometric ratios.
By using complementary property, the value of x for given condition is evaluated as 15.
The missing value x is constituting the angles of both sin and cos trigonometric ratios.
Its known by trigonometry that when [tex]sin(\alpha) = cos(\beta)[/tex], then [tex]\alpha + \beta = 90^{\circ}[/tex]
Thus, we have:
[tex]2x + 7 + 4x - 7 = 90\\\\6x = 90\\\\x = \dfrac{90}{6}\\\\x = 15[/tex]
Thus, value of x for given condition is 15.
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