Evaluate the following$: \frac{\sin 0^{\circ} \sin 35^{\circ} \sin 55^{\circ} \sin 75^{\circ}}{\cos 22^{\circ} \cos 64^{\circ} \cos 58^{\circ} \cos 90^{\circ}}$
View full solution →Question types
Trigonometrical Ratios of Standard Angles question types
145 questions across 4 question groups — pick any mix to generate a MATHEMATICS paper with step-by-step answer keys.
145
Questions
4
Question groups
5
Question types
Sample Questions
Trigonometrical Ratios of Standard Angles questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Evaluate the following$: \tan(78^\circ + \theta ) +\operatorname{cosec}(42^\circ + \theta ) - \cot(12^\circ - \theta ) - \sec(48^\circ - \theta )$
View full solution →Evaluate the following$: \sin(35^\circ + \theta ) - \cos(55^\circ - \theta ) - \tan(42^\circ + \theta ) + \cot(48^\circ - \theta )$
View full solution →Evaluate the following$: \sin35^\circ \sin45^\circ \sec55^\circ \sec45^\circ $
View full solution →Express each of the following in terms of trigonometric ratios of angles between $0^\circ $ and $45^\circ : \cos84^\circ + \operatorname{cosec}69^\circ - \cot68^\circ $
View full solution →If $\sin(\theta - 15^\circ ) = \cos(\theta - 25^\circ ),$ find the value of $\theta $ if $(\theta -15^\circ )$ and $(\theta - 25^\circ )$ are acute angles.
View full solution →If $sec2\theta = cosec3\theta ,$ find the value of \theta if it is known that both $2\theta $ and $3\theta $ are acute angles.
View full solution →If $\tan4\theta = \cot(\theta + 20^\circ ),$ find the value of $\theta $ if $4\theta $ is an acute angle.
View full solution →If $\cos 3\theta = \sin(\theta - 34^\circ ),$ find the value of $\theta $ if $3\theta $ is an acute angle.
View full solution →Evaluate the following: $\frac{3 \sin 37^{\circ}}{\cos 53^{\circ}}-\frac{5 \operatorname{cosec} 39^{\circ}}{\sec 51^{\circ}}+\frac{4 \tan 23^{\circ} \tan 37^{\circ} \tan 67^{\circ} \tan 53^{\circ}}{\cos 17^{\circ} \cos 67^{\circ} \operatorname{cosec} 73^{\circ} \operatorname{cosec} 23^{\circ}}$
View full solution →Evaluate the following:$\frac{5 \cot 5^{\circ} \cot 15^{\circ} \cot 25^{\circ} \cot 35^{\circ} \cot 45^{\circ}}{7 \tan 45^{\circ} \tan 55^{\circ} \tan 65^{\circ} \tan 75^{\circ} \tan 85^{\circ}}+\frac{2 \operatorname{cosec} 12^{\circ} \operatorname{cosec} 24^{\circ} \cos 78^{\circ} \cos 66^{\circ}}{7 \sin 14^{\circ} \sin 23^{\circ} \sec 76^{\circ} \sec 67^{\circ}}$
View full solution →Evaluate the following: $\frac{3 \sin ^2 40^{\circ}}{4 \cos ^2 50^{\circ}}-\frac{\operatorname{cosec}^2 28^{\circ}}{4 \sec ^2 62^{\circ}}+\frac{\cos 10^{\circ} \cos 25^{\circ} \cos 45^{\circ} \operatorname{cosec} 80^{\circ}}{2 \sin 15^{\circ} \sin 25^{\circ} \sin 45^{\circ} \sin 65^{\circ} \sec 75^{\circ}}$
View full solution →Evaluate the following: $\frac{2 \sin 25^{\circ} \sin 35^{\circ} \sec 55^{\circ} \sec 65^{\circ}}{5 \tan 29^{\circ} \tan 45^{\circ} \tan 61^{\circ}}+\frac{3 \cos 20^{\circ} \cos 50^{\circ} \cot 70^{\circ} \cot 40^{\circ}}{5 \tan 20^{\circ} \tan 50^{\circ} \sin 70^{\circ} \sin 40^{\circ}}$
View full solution →Evaluate the following: $\frac{5 \sec 68^{\circ}}{\operatorname{cosec} 22^{\circ}}+\frac{3 \sin 52^{\circ} \sec 38^{\circ}}{\cot 51^{\circ} \cot 39^{\circ}}$
View full solution →If $A+B=90^{\circ}$, prove that $\frac{\tan A \tan B+\tan A \cot B}{\sin A \sec B}-\frac{\sin ^2 B}{\cos ^2 A}=\tan ^2 A$
View full solution →In the given figure, $\angle B =60^{\circ}, \angle C =30^{\circ}, AB =8 \ cm$ and $BC =24 \ cm$. Find$:\ a. BE,b. AC$
View full solution →Find the length of $EC.$
View full solution →In a trapezium $\text{ABCD}$, as shown, $AB \| DC, AD = DC = BC = 24 \ cm$ and $\angle A = 30^\circ $. Find: length of $AB$
View full solution →Find lengths of diagonals $AC$ and $BD$. Given $AB = 24 \ cm$ and $\angle BAD = 60^\circ .$
View full solution → In the given figure, a rocket is fired vertically upwards from its launching pad $P$. It first rises $20 \ km$ vertically upwards and then $20 \ km$ at $60^\circ $ to the vertical. $PQ$ represents the first stage of the journey and $QR$ the second. $S$ is a point vertically below $R$ on the horizontal level as $P$, find$:\ a$. the height of the rocket when it is at point $R.b.$ the horizontal distance of point $S$ from $P.$
View full solution →Generate a Trigonometrical Ratios of Standard Angles paper free
Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.