To solve the given problem, we should start by analyzing the trigonometric equation and finding the required angle.
- Given: \cos 2\theta = 0.
- To find the value of \theta satisfying this equation with \theta as an acute angle, we use the property:
- \cos 2\theta = 0 implies 2\theta = 90^\circ.
- Therefore, \theta = \frac{90^\circ}{2} = 45^\circ.
- Now, we need to find \sin(75^\circ - \theta):
- Substitute the value of \theta:
- \theta = 45^\circ; hence, we need \sin(75^\circ - 45^\circ) = \sin(30^\circ).
- Using the known trigonometric value: \sin(30^\circ) = \frac{1}{2}.
- Therefore, the value of \sin(75^\circ - \theta) is \frac{1}{2}.
Hence, the correct answer is \frac{1}{2}.
Similar Questions
- If $8 \tan A = 5$, what is the value of $\frac{8\sin A - 7\cos A}{8\sin A + 11\cos A}$?
- Find the value of $\frac{\cos 25^\circ - \sin 65^\circ}{\cos 25^\circ + \sin 65^\circ}$
- If $\sin(5x - 40^\circ) = \cos (5y + 40^\circ)$, then the value of $x + y$ is:
Evaluate. $(\frac{\sin 23^\circ \cos 67^\circ+\cos 23^\circ \sin 67^\circ}{\text{cosec}^2 15^\circ- \tan^2 75^\circ})^3$
- The sides of a right-angled triangle, right-angled at B, are 6, 8 and 10 units. C is the vertex opposite to the side with length 8 units. What is the value of $\tan^2 A + \cos^2 C$?
- If $\mu = 60^\circ$, then $\sin\mu + \cos(90^\circ - \mu) = $
- The expression $sin^2 \theta + cos^2 \theta - 1 = 0$ is satisfied by how many values of $\theta$?
- Find the value of (sin $75^\circ$ + sin $15^\circ$).
Evaluate the following.
$$\frac{5\cos^2 120^\circ + 4\sec^2 30^\circ - \tan^2 135^\circ} {\sin^2 30^\circ + \cos^2 30^\circ}$$
- Evaluate $7\left(\frac{\text{cosec } 24^\circ}{\text{sec } 66^\circ}\right)^3 + 8\left(\frac{\text{cot } 37^\circ}{\text{tan } 53^\circ}\right)^4 - \left(2\frac{\text{sec } 14^\circ}{\text{cosec } 76^\circ}\right)^2 + \left(-3\frac{\text{tan } 82^\circ}{\text{cot } 8^\circ}\right)^3$.
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
The value of sin θ and cos θ when the angle θ is 0 ≤ θ ≤ 90°, is ______
