The problem asks for the value of $x - y$ given the trigonometric equation:
$ \sin(3x - 20)^\circ = \cos(20 - 3y)^\circ $
Using Trigonometric Identities to Solve for x - y
We can use the co-function identity $\sin(\theta) = \cos(90^\circ - \theta)$. Apply this to the left side of the equation:
- $ \cos(90^\circ - (3x - 20^\circ)) = \cos(20 - 3y)^\circ $
- $ \cos(90^\circ - 3x + 20^\circ) = \cos(20 - 3y)^\circ $
- $ \cos(110^\circ - 3x) = \cos(20 - 3y)^\circ $
Since the cosine values are equal, the angles must be related. Assuming the simplest case where the angles are equal:
- $ 110^\circ - 3x = 20 - 3y $
Rearrange the equation to solve for $x - y$:
- $ 110^\circ - 20^\circ = 3x - 3y $
- $ 90^\circ = 3(x - y) $
- $ x - y = \frac{90^\circ}{3} $
- $ x - y = 30^\circ $
Therefore, the value of $x - y$ is $30^\circ$.
Similar Questions
- If $r\sin\theta = \frac{7}{2}$ and $r\cos\theta = \frac{7\sqrt{3}}{2}$, then what will be the value of r?
- If $\sin \theta + \text{cosec } \theta = \sqrt{5}$, then the value of $\sin^3 \theta + \text{cosec}^3 \theta$ is:
- If $x + y = 75$ and $\sin x : \sin y = \frac{1}{\sqrt{2}} : \frac{1}{2}$, then $x : y$ is:
- If $(1 + \tan A)(1 + \tan B) = 2$, then what will be the value of $\tan(A+B)$?
- The value of $\frac{\tan 45^\circ - \tan 30^\circ}{1 + \tan 45^\circ \tan 30^\circ}$ is :
- Angle $54^\circ$ is equivalent to (in radians):
- If $\cos x=-\frac{3}{5}$ and $x$ lies in the third quadrant, then the value of the $\sin x$ is:
- If $\sin(x - y) = \frac{\sqrt{3}}{2}$ and $\cos(x + y) = \frac{1}{2}$, where x and y are positive acute angles and $x \ge y$, then the value of $x$ is:
- If $\sin\theta - \cos\theta = \frac{\sqrt{3}}{2}$, then find the positive value of $\sin\theta + \cos\theta$.
- If $\sin \theta + \cos \theta = \frac{\sqrt{7}}{2}$, then find the value of $\sin \theta - \cos \theta$.
Important Questions from Trigonometry
The given equation can be reduced to
If sin2x = a - b√c, where a and b are natural numbers and c is prime number, then what is the value of a - b + 2c ?
If \(\sin θ = \frac{8}{{17}}\) , then find the value of tan θ.
If cos(A - B) = \(\frac{\sqrt 3}{2}\) and cot(A + B) = \(\frac{1}{\sqrt 3}\) , Where A - B and A + B are acute angles, then (2A - 3B) is equal to:
If 3 tanθ = \(2\sqrt 3 \) sinθ, 0° < θ < 90°, then the value of \(\rm \frac{{\cos e{c^2}2\,\theta + {{\cot }^2}2\,\theta }}{{{{\sin }^2}\,\theta + {{\tan }^2}2\,\theta }}\) is:
