Sample QuestionsTrigonometric Ratios Of Multiple And Sub Multiple Angles questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If in $\text{a}\triangle\text{ABC},\tan\text{B}+\tan\text{C}=6,$ then $\cot\text{A}\cot\text{B}\cot\text{C}=$
Answer: C.
View full solution →If $\tan\theta_1\tan\theta_2=\text{k},$ then $\frac{\cos(\theta_1-\theta_2)}{\cos(\theta_1+\theta_2)}=$
- ✓
$\frac{1+\text{k}}{1-\text{k}}$
- B
$\frac{1-\text{k}}{1+\text{k}}$
- C
$\frac{\text{k}+1}{\text{k}-1}$
- D
$\frac{\text{k}-1}{\text{k}+1}$
Answer: A.
View full solution →If $\text{A}-\text{B}=\frac\pi4,$ then $(1+\tan\text{A})(1-\tan\text{B})$ is equal to:
Answer: A.
View full solution →The value of $\cos^2\Big(\frac{\pi}{6}+\text{x}\Big)-\sin^2\Big(\frac\pi6-\text{x}\Big)$ is:
Answer: A.
View full solution →If $\tan69^\circ+\tan66^\circ-\tan69^\circ\tan66^\circ=2\text{k},$ then k =
- A
$-1$
- B
$\frac12$
- ✓
$\frac{-1}{2}$
- D
Answer: C.
View full solution →If $\tan(\text{A+B})=\text{p}$ and $\tan\text{(A - B)}=\text{q},$ then write the value of $\tan2\text{B}.$
View full solution →Write the maximum and minimum values of $3\cos\text{x}+4\sin\text{x}+5.$
View full solution →Evaluate the following:
$\cos47^\circ\cos13^\circ-\sin47^\circ\sin13^\circ$
View full solution →Evaluate the following:
$\cos80^\circ\cos20^\circ+\sin80^\circ\sin20^\circ$
View full solution →If $\text{x}\cos\theta=\text{y}\cos\Big(\theta+\frac{2\pi}{3}\Big)=\text{z}\Big(\theta+\frac{4\pi}{3}\Big),$ then write the value of $\frac{1}{\text{x}}+\frac{1}{\text{y}}+\frac{1}{\text{z}}.$
View full solution →Prove that:$\frac{\tan69^\circ+\tan66^\circ}{1-\tan69^\circ\tan66^\circ}=-1$
View full solution →If $\frac{\sin(\text{x}+\text{y})}{\sin(\text{x}-\text{y)}}=\frac{\text{a}+\text{b}}{\text{a}-\text{b}}$ show that $\frac{\tan\text{x}}{\tan\text{y}}=\frac{\text{a}}{\text{b}}.$
View full solution →Prove that: $\tan\frac{\pi}{12}+\tan\frac{\pi}{6}+\tan\frac{\pi}{12}\tan\frac{\pi}{6}=1$
View full solution →Prove that: $\cos\frac{7\pi}{12}+\cos\frac{\pi}{12}=\sin\frac{5\pi}{12}-\sin\frac{\pi}{12}$
View full solution →Prove that:
$\sin\Big(\frac{3\pi}{8}-\text{5}\Big)\cos\Big(\frac{\pi}{8}+\text{5}\Big)+\cos\Big(\frac{3\pi}{8}-\text{5}\Big)\sin\Big(\frac{\pi}{8}+\text{5}\Big)=1$
View full solution →Prove that: $\frac{\tan^22\text{x}-\tan^2\text{x}}{1-\tan^22\text{x}\tan^2\text{x}}=\tan3\text{x}\tan\text{x}$
View full solution →If $\sin\text{A}=\frac{1}{2},$ $\cos\text{B}=\frac{\sqrt{3}}{2},$ where $\frac{\pi}{2}<\text{A}<\pi$ and $0<\text{B}<\frac{\pi}{2},$find the following:$\tan{\text{(A+B)}}$
View full solution →If $\sin\text{A}=\frac{4}{5}$ and $\cos\text{B}=\frac{5}{13}$ Where $0<\text{A},\text{B}<\frac{\pi}{2},$ find the value of the following:
View full solution →Prove that: $\tan36^\circ+\tan9^\circ+\tan36^\circ+\tan9^\circ=1$
View full solution →If $\cos\text{A}=-\frac{24}{25},$ $\cos\text{B}=-\frac{12}{13},$ where $A$ and $B$ both lie in second quadrant,find the value of $\sin\text{(A+B)}$.
- $\sin\text{(A+B)}$
- $\cos\text{(A+B)}$
View full solution →Find the maximum and minimum values of each of the following trigonometrical expressions:
$\sin\text{x}-\cos\text{x}+1$
View full solution →Prove that:$\sin^2\text{B}=\sin^2\text{A}+\sin^2\text{(A}-\text{B)}-2\sin\text{A}\cos\text{B}\sin\text{(A}-\text{B)} $
View full solution →Prove that:
$\frac{1}{\cos\text{(x}-\text{b})\cos\text{(x}-\text{b)}}=\frac{\tan\text{(x}-\text{a)}-\tan\text{(x}-\text{b)}}{\sin\text{(a}-\text{b)}}$
View full solution →If $\alpha\text{ and }\beta$ are two solutions of the equation $\text{a}\tan\text{x+b}\sec\text{x}=\text{c},$ the find the value of $\sin(\alpha+\beta)\text{ and }\cos(\alpha+\beta).$
View full solution →If $\sin(\alpha+\beta)=1$ and $\sin(\alpha-\beta)=\frac{1}{2}$ where $0\leq\alpha,\beta\leq\frac{\pi}{2}$ than find the values of $\tan(\alpha+2\beta)$and $\tan(2\alpha+\beta).$
View full solution →