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 $(1 + \tan A)(1 + \tan B) = 2$, 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 :
- If $\cos\theta + \sec\theta = \sqrt{3}$, then the value of $\cos^3\theta + \sec^3\theta$ is:
- Angle $54^\circ$ is equivalent to (in radians):
- If $x + y = 75$ and $\sin x : \sin y = \frac{1}{\sqrt{2}} : \frac{1}{2}$, then $x : y$ is:
- If $\sin \theta + \text{cosec } \theta = \sqrt{5}$, then the value of $\sin^3 \theta + \text{cosec}^3 \theta$ is:
- If $\cot 3\theta \cot 6\theta = 1$, then the value of $\tan 15\theta$ will be:
- If $\cos x + \frac{1}{\cos x} = 2$ then find the value of $\cos^n x + \frac{1}{\cos^n x}$
- If $a \tan \alpha = b$, then the value of $\cos \alpha$ will be:
- If $\sin\theta - \cos\theta = \frac{\sqrt{3}}{2}$, then find the positive value of $\sin\theta + \cos\theta$.
Important Questions from Trigonometry
(secθ + tanθ)/(secθ - tanθ) is equal to:
If tan 45°, cot θ then the value of θ, in radians is
ABC is a triangle If sin (A+B)/2 = √3/2, then the value of sin C/2 is
The angles of elevation of the top of a temple, from the foot and the top of a building 30 m high, are 60° and 30° respectively. Then height of the temple is
what is the principal value of \(\sin^{-1} \left( \sin \dfrac{2 \pi}{3} \right)\) ?
