Aptitude Question ID : 94464

$latex \sin ^{2}5^{\circ}+\sin ^{2}10^{\circ}+\sin ^{2}15^{\circ}+……+\sin ^{2}85^{\circ}+\sin ^{2}90^{\circ}$ is equal to : [A]$latex 7\frac{1}{2}&s=1$ [B]$latex 8\frac{1}{2}&s=1$ [C]$latex 9\frac{1}{2}&s=1$ [D]$latex 9$ Show Answer $latex \mathbf{9\frac{1}{2}}&s=1$ $latex \sin \Theta = \cos\Theta (90^{\circ}-\Theta);$ $latex \sin (90^{\circ}-\Theta) = \cos\Theta$ $latex \therefore \sin 85^{\circ} = \sin (90^{\circ}-5^{\circ}) = \cos5^{\circ}$ $latex \mathbf{\therefore (\sin^{2}5^{\circ}+\sin^{2}85^{\circ})+(\sin^{2}10^{\circ}+\sin^{2}80^{\circ})+…. to 8 terms +(\sin^{2}45^{\circ}+\sin^{2}90^{\circ})}$ $latex = 8\times 1 + ..

Aptitude Question ID : 94460

If $latex \angle A$ and $latex \angle B$ are complementary to each other, then the value of $latex \sec ^{2}A+\sec ^{2}B-\sec ^{2}A\cdot \sec ^{2}B$ is : [A]-1 [B]0 [C]1 [D]2 Show Answer 0 $latex \angle A +\angle B = 90^{\circ}$ $latex => \angle B = 90^{\circ}- \angle A$ $latex \therefore \sec ^{2}A+\sec ^{2}B-\sec ^{2}A\cdot \sec ..

Aptitude Question ID : 94453

If $latex \theta$ be an acute angle and $latex 7\sin ^{2}\theta+3\cos ^{2}\theta = 4,$ then the value of $latex \tan \theta$ is: [A]$latex 0$ [B]$latex \frac{1}{\sqrt{3}}&s=1$ [C]$latex 1$ [D]$latex \sqrt{3}$ Show Answer $latex \mathbf{\frac{1}{\sqrt{3}}}&s=1$ $latex 7\sin ^{2}\Theta+3\cos ^{2}\Theta = 4$ $latex => 7\frac{\sin^{2}\Theta}{\cos^{2}\Theta}+3 = \frac{4}{\cos^{2}\Theta} = 4\sec^{2}\Theta&s=1$ $latex => 7\tan^{2}\Theta+3 = 4(1+\tan^{2}\Theta)$ $latex => 7\tan^{2}\Theta-4\tan^{2}\Theta= ..

Aptitude Question ID : 94449

The value of $latex \cot 10^{\circ}\cdot \cot 20^{\circ}\cdot \cot 60^{\circ}\cdot \cot 70^{\circ}\cdot \cot 80^{\circ}$ is : [A]-1 [B]1 [C]$latex \frac{1}{\sqrt{3}}&s=1$ [D]$latex \sqrt{3}$ Show Answer $latex \mathbf{\frac{1}{\sqrt{3}}}&s=1$ $latex \cot 10^{\circ}\cdot \cot 80^{\circ}\cdot \cot 20^{\circ}\cdot \cot 70^{\circ}\cdot \cot 60^{\circ}$ $latex = \cot 10^{\circ}\cdot \tan 10^{\circ}\cdot \cot 20^{\circ}\cdot \tan 20^{\circ}\cdot \cot 60^{\circ}$ $latex \left [ \because \tan\left ( ..

Aptitude Questions : 94446

The angles of a triangle are $latex (x+5)^{\circ}, (2x-3)^{\circ}$ and $latex (3x+4)^{\circ}.$ The value of x is : [A]28 [B]29 [C]30 [D]31 Show Answer 29 Sum of angles of a triangle $latex = 180^{\circ}$ $latex \therefore x+5+2x-3+3x+4 = 180^{\circ}$ $latex => 6x+6 = 180^{\circ}$ $latex => 6x = 180 – 6 = 174^{\circ}$ $latex => ..