Trigonometry

Quantitative Aptitude Questions and Answers section on “Trigonometry” with solution and explanation for competitive examinations such as CAT, MBA, SSC, Bank PO, Bank Clerical and other examinations.

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 => ..