Sample QuestionsTrigonometrical Ratios questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Without using trigonometric tables, evaluate.
$\cos ^2 24+\cos ^2 66$
View full solution →Without using trigonometric tables, evaluate.
$\operatorname{cosec}^2 48-\tan ^2 52$
View full solution →Without using trigonometric tables, evaluate.
$\sec ^2 36-\cot ^2 54$
View full solution →Without using trigonometric tables, evaluate.
$\sin ^2 23+\sin ^2 67$
View full solution →Without using trigonometric tables, evaluate.
$\cos ^2 25-\sin ^2 65$
View full solution →Express the following in terms of trigonometric ratios of angles between 0 and 45.
$\sin 59+\cos 56$
View full solution →Express he following in terms of trigonometric ratios of angles between 0 and 45.
$\sec 63+\operatorname{cosec} 49$
View full solution →Express the following in terms of trigonometric ratios of angles between 0 and 45.
$\cos 76+\sec 76$
View full solution →Express the following in terms of trigonometric ratios of angles between 0 and 45.
$\cos 81+\cot 81$
View full solution →Without using trigonometric table, prove that :
$\tan 10 \tan 15 \tan 75 \tan 80=1$
View full solution →Prove that $: \tan \left(45^{\circ}- A \right) \tan \left(45^{\circ}+ A \right)=1$.
$\left[\right.$ Hint . $\left.\tan \left(45^{\circ}- A \right)=\tan \left[90^{\circ}-\left(45^{\circ}+ A \right)\right]=\cot \left(45^{\circ}+ A \right)\right]$.
View full solution →Prove that : $\sin \left(50^{\circ}+\theta\right)-\cos \left(40^{\circ}-\theta\right)=0$.
$\left[\right.$ Hint . $\left.\sin \left(50^{\circ}+\theta\right)=\sin \left\{90^{\circ}-\left(40^{\circ}-\theta\right)\right\}\right]$
View full solution →If $0^{\circ}<\theta<25^{\circ}$, prove that $\cos \left(65^{\circ}+\theta\right)-\sin \left(25^{\circ}-\theta\right)=0$.
View full solution →Without using tables, verify that:
$\cos 60^{\circ}=\frac{1-\tan ^2 30^{\circ}}{1+\tan ^2 30^{\circ}}=\frac{1}{2}$.
View full solution →Without using tables, verify that:
$\sin 60^{\circ}=\frac{2 \tan 30^{\circ}}{1+\tan ^2 30^{\circ}}=\frac{\sqrt{3}}{2}$.
View full solution →In a rectangle $ABCD , AB =12 cm$ and $\angle BAC =30$. Calculate the lengths of side BC and diagonal AC.
View full solution →In a $\triangle A B C$, right angled at $B$, if $\angle A=30$ and $B C=8 cm$, find the remaining angles and sides.
View full solution →A kite is flying at a height of 120 m from the level ground. It is attached to a string inclined at 60 to the horizontal. Find the length of the string. (Take $\sqrt{3}=1.73$.)
View full solution →A kite is flying with a thread 150 m long. If the thread is assumed stretched straight and makes an angle of 60 with the horizontal, find the height of the kite above the ground. (Take $\sqrt{3}=1.73$.)
View full solution →A ladder leaning against a wall, makes a angle of 60 with the horizontal and the foot of the ladder is 9.5 metres away from the wall. Find the length of the ladder.
Assertion (A) : $\frac{\sin 27^9}{\cos 63^2}=1$
Reason (R) : $\sin (90-\theta)=\cos \theta$ and $\cos (90-\theta)=\sin \theta$.
Answer: C.
View full solution →Assertion (A) : In a right angled $\triangle ABC$, if $\angle ABC =90, AB =3 cm, BC =4 cm$, then $\sin A=\cos C$.
Reason (R) : $\frac{\sin \theta}{\cos \theta}=\tan \theta$ and $\sin \theta \quad \cos \theta=\cot \theta$.
Answer: A.
View full solution →Assertion (A) : The value of $\sin 60 \cos 30+\cos 60 \sin 30$ is 0 .
Reason (R) : $\sin 90=0$ and $\sin 0=1$.
Answer: D.
View full solution →The value of $\left(\cos 0^{\circ}+\sin 45^{\circ}+\sin 30^{\circ}\right)\left(\sin 90^{\circ}-\cos 45^{\circ}+\cos 60^{\circ}\right)=$
- A
$\frac{3}{5}$
- B
$\frac{5}{6}$
- ✓
$\frac{7}{4}$
- D
$\frac{5}{8}$
Answer: C.
View full solution →The value of $\tan 5 \tan 25 \tan 30^{\circ} \tan 65 \tan 85=$
- A
- B
$\sqrt{3}$
- ✓
$\frac{1}{\sqrt{3}}$
- D
Answer: C.
View full solution →