Find the value of \(\theta\) if:
1) \(\cos \theta = \frac{1}{\sqrt{2}}\)
2) \(\tan \theta = 1\)
Either 1 or 2 is sufficient.
Statement 1 alone: cos θ = 1/√2 → θ = 45° (in principal range).
Statement 2 alone: tan θ = 1 → θ = 45° (in principal range).
Each statement alone is sufficient to determine θ = 45°.
Hence, Either 1 or 2 is sufficient..
Similar Questions
If \(\sin\theta + \cos\theta = \frac{7}{17}\), then find the positive value of \(\sin\theta - \cos\theta\).
If \(\sin\theta + \cos\theta = \sqrt{2}\), then find the value of \(\tan\theta + \cot\theta\).
In ∆ABC, ∠C = 90°, and tanA = \(\sqrt{6}\), then find the value of sinA × cosB × cosec(A + B).
If sinθ + cosecθ = \(\sqrt{5}\), then find the value of sin3θ + cosec3θ.
\(\frac{\cot 45^\circ}{1 + \sin 45^\circ} + \frac{1 + \sin 45^\circ}{\cot 45^\circ} = ?\)
The sum of the values of all the six trigonometric ratios when the angle \(\alpha = 45^\circ\) is:
If \(\tan A = 8/7\), find \([(1 + \sin A)(1 - \sin A)] / [(1 + \cos A)(1 - \cos A)]\).
If \(\alpha\) and \(\beta\) are complementary angles and \(\operatorname{cosec} \alpha = \frac{5}{3}\), find the value of \(\sin \alpha \cos \beta - \cos \alpha \sin \beta\).
\(\frac{\tan 45^\circ}{1 + \cos 45^\circ} + \frac{1 + \sin 45^\circ}{\cot 45^\circ} = ?\)
The angle of depression from the top of a tower to the foot of a building 36 metres away is \(30^{\circ}\). What is the height of the tower?
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 ______
