The value of the expression \(\rm \frac{4\sin^230^{\circ}+\cos^260^{\circ}-\tan^245^{\circ}}{2\sin60^{\circ}\cos30^{\circ}-\tan45^{\circ}}\) is:
The correct answer is \frac{1}{2}.
Revision Table: Standard Trigonometric Values Angle (\theta) \sin \theta \cos \theta \tan \theta 0^{\circ} 0 1 0 30^{\circ} \frac{1}{2} \frac{\sqrt{3}}{2} \frac{1}{\sqrt{3}} 45^{\circ} \frac{1}{\sqrt{2}} \frac{1}{\sqrt{2}} 1 60^{\circ} \frac{\sqrt{3}}{2} \frac{1}{2} \sqrt{3} 90^{\circ} 1 0 Undefined Additional Information on Trigonometric Expressions Evaluating trigonometric expressions often involves knowing the values of trigonometric functions for common angles, like those found in special right triangles (30-60-90 and 45-45-90 triangles). Remember the identities such as \sin^2\theta + \cos^2\theta = 1 and \tan\theta = \frac{\sin\theta}{\cos\theta} can also be useful when simplifying more complex expressions. Practice using these standard values and identities to quickly solve problems involving trigonometric expressions.
Similar Questions
If tan 3 θ = cot(θ - 22°), where 3 θ is an angle, find the value of θ.
The value of cot (-315°) is :
The value of \(\frac{\tan^2 (22^\circ - \theta)-\tan (\theta + 68^\circ)\ -\ \text{cosec}^2 (68^\circ + \theta)+\cot (22^\circ - \theta)} {3 (\cot^2 52^\circ - \sec^2 38^\circ)+ 2 (\text{cosec}^2 \ 28^\circ - \tan^2 62^\circ)}\) is:
The value of \(\frac{{{{\sec }^2}60^\circ {{\cos }^2}45^\circ \, + \,{\rm{cose}}{{\rm{c}}^2}30^\circ }}{{{{\sec }^2}45^\circ - \tan 45^\circ }}\) is:
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sinθ + cosec θ = 2, then the value of sin 99 θ + cosec 99 θ is:
If cos θ = \(\frac{5}{13}\) , what is the value of cot θ ?
Determine the largest angle if the angles of a triangle are in the ratio 3 : 4 : 5.
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Important Questions from Circular Measure of Angles
Which of the following values of A and B satisfies, sin(A + B) = sin A + sin B, where
If tan 3 θ = cot(θ - 22°), where 3 θ is an angle, find the value of θ.
The value of 4cos\(\left( {\frac{\pi }{6}\, - \,\alpha } \right)\) sin\(\left( {\frac{\pi }{3}\, - \,\alpha } \right)\) is equal to:
1 + tan 15° cot 75° is equal to:
If tan θ = 1/√5, find the value of cosec2θ – sec2θ.
