What is the <strong>MAXIMUM</strong> value of 1+2\sin^{2}\theta\cos^{2}\theta-\sin^{4}\theta-\cos^{4}\theta where 0^{\circ}\lt\theta\lt90^{\circ}?

Explanation

The expression can be rewritten as 1 - (\sin^4\theta - 2\sin^2\theta\cos^2\theta + \cos^4\theta) = 1 - (\sin^2\theta - \cos^2\theta)^2 = 1 - \cos^2 2\theta = \sin^2 2\theta. The maximum value of \sin^2 2\theta is 1, which occurs at \theta = 45^{\circ}.

Related questions on Trigonometry

• Two poles are situated 24 m apart and their heights differ by 10 m. What is the distance between their tips?
• If \frac{\cos \theta}{1 - \sin \theta} + \frac{\cos \theta}{1 + \sin \theta} = 4, then which one of the following is a value of $(\tan^2 \...
• For 0 < \theta < \frac{\pi}{2}, consider the following : I. $(\tan^4 \theta + \tan^6 \theta)(\cot^4 \theta + \cot^6 \theta) = \sec^2 \the...
• If 3\sin \theta + 4\cos \theta = 5, then what is a value of 4\tan \theta + 3\cot \theta ?
• At a point on level ground, the tangent of the angle of elevation of the top of a tower is found to be \frac{5}{6}. On walking 70 m toward...