Sample QuestionsTrigonometric Ratios Of Compound Angles questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The value of $\frac{\sin5\alpha-\sin\beta}{\cos5\alpha+2\cos4\alpha+\cos3\alpha}$ is :
- A
$\cot\frac{\alpha}{2}$
- B
$\cot\alpha$
- ✓
$\tan\frac{\alpha}{2}$
- D
Answer: C.
View full solution →The value of $\tan\text{x}+\tan\Big(\frac{\pi}{3}+\text{x}\Big)+\tan\Big(\frac{2\pi}{3}+\text{x}\Big)$ is :
- ✓
$3\tan3\text{x}$
- B
$\tan3\text{x}$
- C
$3\cot3\text{x}$
- D
$\cot3\text{x}$
Answer: A.
View full solution →The value of $\Big(\cot\frac{\text{x}}{2}-\tan\frac{\text{x}}{2}\Big)^2(1-2\tan\text{x}\cot2\text{x})$ is :
Answer: D.
View full solution →If $\tan\text{X}=\frac{\text{a}}{\text{b}},$ then $\text{b}\cos2\text{x}+\text{a}\sin2\text{x}$ is equal to :
Answer: B.
View full solution →The value of $\sin^2\Big(\frac{\pi}{18}\Big)+\sin^2\Big(\frac{\pi}{9}\Big)+\sin^2\Big(\frac{7\pi}{18}\Big)+\sin^2\Big(\frac{4\pi}{9}\Big)$ is :
Answer: B.
View full solution →If $\tan\frac{\text{x}}{2}=\frac{\text{m}}{\text{n}},$ then write the value of $\text{m}\ \sin\text{x}+\text{n}\cos\text{x}.$
View full solution →Prove that:
$\frac{\sin2\text{x}}{1-\cos2\text{x}}=\cot\text{x}$
View full solution →Prove that:
$\sqrt{\frac{1-\cos2\text{x}}{1+\cos2\text{x}}}=\tan\text{x}$
View full solution →Write the angled triangle ABC, write value of $\sin^2\text{A}\sin^2\text{B}+\sin^2\text{C}.$
View full solution →If $\frac{\pi}{2}<\text{x}<\pi,$ then wrire the value of $\sqrt{\frac{1-\cos^2\text{x}}{1+cos^2\text{x}}}.$
View full solution →Prove that:
$\sqrt{2+\sqrt{2+2\cos4\text{x}}}=2\cos\text{x},0\cos\text{x},<\text{x}<\frac{\pi}{4}$
View full solution →If $\cos\text{x}=\frac{4}{5}$ and x is acute, find $\tan 2\text{x}$
View full solution →Prove that:
$\frac{\cos2\text{x}}{1+\sin2\text{x}}=\tan(\frac{\pi}{4}-\text{x})$
View full solution →Prove that:
$\cos^2\frac{\pi}{8}+\cos^2\frac{3\pi}{8}+\cos^2\frac{5\pi}{8}+\cos^2\frac{7\pi}{8}=2$
View full solution →If $\text{a}\cos2\text{x}+\text{b}\sin2\text{x}=\text{c}$ has $\alpha$ and $\beta$ as its roots, then prove that,
$\tan(\alpha+\beta)=\frac{\text{b}}{\text{a}}$
View full solution →Prove that:
$\cot^2\text{x}-\tan^2\text{x}=4\cot2\text{x}\ \text{cosec}\ 2\text{x}$
View full solution →If $\tan\text{x}=\frac{\text{b}}{\text{a}},$ then find the value of $\sqrt{\frac{\text{a+b}}{\text{a}-\text{b}}}+\sqrt{\frac{\text{a}-\text{b}}{\text{a}+\text{b}}}$
View full solution →Prove that
$\cos\frac{\pi}{5}\cos\frac{2\pi}{5}\cos\frac{\pi}{5}\cos\frac{8\pi}{5}=\frac{-1}{16}$
View full solution →Prove that:
$\big(\cos\alpha+\cos\beta^2\big)+\big(\sin\alpha+\sin\beta\big)^2=2\cos^2\Big(\frac{\alpha-\beta}{2}\Big)$
View full solution →Prove that:
$\sin4\text{x}=4\sin\text{x}\cos^3\text{x}-4\cos\text{x}\sin^3\text{x}$
View full solution →$\Bigg|\sin\text{x}\sin\Big(\frac{\pi}{3}-\text{x}\Big)\sin\Big(\frac{\pi}{3}+\text{x}\Big)\Bigg|\not<\frac{1}{4}$ for all values of x.
View full solution →If $\text{a}\cos2\text{x}+\text{b}\sin2\text{x}=\text{c}$ has $\alpha$ and $\beta$ as its roots, then prove that,
$\tan\alpha+\tan\beta=\frac{2\text{b}}{\text{a+c}}$
View full solution →Prove that
$\cos\frac{2\pi}{15}\cos\frac{4\pi}{15}\cos\frac{8\pi}{15}\cos\frac{16\pi}{15}=\frac{1}{16}$
View full solution →Prove that
$\cos\frac{\pi}{65}\cos\frac{2\pi}{65}\cos\frac{4\pi}{65}\cos\frac{8\pi}{65}\cos\frac{16\pi}{65}\cos\frac{32\pi}{65}=\frac{1}{64}$
View full solution →If $0\leq\text{x}\leq\pi$ and x lies in the IInd quadrant such that $\sin\text{x}=\frac{1}{4}.$ Find the values of $\cos\frac{\text{x}}{2},\sin\frac{\text{x}}{2}$ and $\tan\frac{\text{x}}{2}$
View full solution →$\sin5\text{x}=5\cos^4\text{x}\sin\text{x}-10\cos^2\text{x}\sin^3\text{x}+\sin^5\text{x}$
View full solution →Prove that:
$\cos\frac{\pi}{15}\cos\frac{2\pi}{15}\cos\frac{3\pi}{15}\cos\frac{4\pi}{15}\cos\frac{5\pi}{15}\cos\frac{6\pi}{15}\cos\frac{7\pi}{15}=\cos\frac{1}{128}$
View full solution →$\tan\text{x}\tan(\text{x}+\frac{\pi}{3})+\tan\text{x}(\frac{\pi}{3}-\text{x})\\+\tan(\text{x}+\frac{\pi}{3})\tan(\text{x}-\frac{\pi}{3})=-3$
View full solution →