Sample QuestionsTrigonometric Ratios Of Compounds 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 →$\sin5\text{x}=5\cos^4\text{x}\sin\text{x}-10\cos^2\text{x}\sin^3\text{x}+\sin^5\text{x}$
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 →$\Bigg|\sin\text{x}\sin\Big(\frac{\pi}{3}-\text{x}\Big)\sin\Big(\frac{\pi}{3}+\text{x}\Big)\Bigg|\not<\frac{1}{4}$ 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 →