Answer:
x=9.29
Step-by-step explanation:
[tex]\boxed{Formula \:used:\: cos\theta = sin(90\degree-\theta)}\\\sin (2 x + 5)\degree = \cos (5 x +20)\degree\\\sin (2 x + 5)\degree = \sin\{90- (5 x +20)\}\degree\\ (2 x + 5)\degree = \{90- (5 x +20)\}\degree\\\\ (2 x + 5) = 90- (5 x +20)\\ (2 x + 5) + (5 x +20) = 90\\7x+25=90\\7x= 90-25\\7x=65\\x=\frac{65}{7} \\x=9.285714285\\x=9.29[/tex]
The relation between the sine and cosine is used to solve the problem. Then the value of x is 9.29.
Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
If sin (2 x + 5)° = cos (5 x +20)°. Then the value of x will be
We know
sin θ = cos (90 - θ)
Then we have
cos (90 - 2x - 5)° = cos (5x +20)°
Then take cosine inverse on both sides, then we have
90 - 2x - 5 = 5x + 20
7x = 65
x = 9.2857 ≅ 9.29
More about the trigonometry link is given below.
https://brainly.com/question/22698523
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