Sum of Cosines of Angles in Arithmetic Progression

Q. In ∆ ABC, if a = 18, b = 24 and c = 30, find cos A, cos B and cos C.

Q. $\cos \frac{\pi }{6}\cos \frac{\pi }{3}\cos \frac{4\pi }{6}\cos \frac{8\pi }{6}\cos \frac{16\pi }{6}\cos \frac{32\pi }{6}=$

1. $\frac{\sqrt{3}}{32}$
2. $\frac{\sqrt{3}}{64}$
3. $\frac{\sqrt{3}}{8}$
4. $\frac{\sqrt{3}}{16}$

Q. If α + β = 90°, show that the maximum value of cos α cos β is $\frac{1}{2}$.

Q. If α + β = $\frac{\pi }{2}$, show that the maximum value of cos α cos β is $\frac{1}{2}$.

Q.

$Ify=3^{lo{g}_9^{(1+ta{n}^{2}z)}}then\frac{dy}{dx}=$

1. SecX

2. tanx

3. 2Sec²x tanx

4. Secx tanx

Q. Find the general solutions of the following equations:
(i) $\sin x=\frac{1}{2}$

(ii) $\cos x=-\frac{\sqrt{3}}{2}$

(iii) $\mathrm{cosec}x=-\sqrt{2}$

(iv) $\sec x=\sqrt{2}$

(v) $\tan x=-\frac{1}{\sqrt{3}}$

(vi) $\sqrt{3}\sec x=2$

Q. The value B $={\int }_1^{100}\left[se{c}^{-1}x\right]$ dx (where [.] denotes greatest integer funciton) is equal to

1. $sec1$
2. $100-sec1$
3. $99-sec1$
4. $sec1-100$

Q. Solve this :


$\mathit{P}\mathit{r}\mathit{o}\mathit{v}\mathit{e}\mathbf{}\mathit{t}\mathit{h}\mathit{a}\mathit{t}\mathbf{}\mathbf{}\frac{\mathbf{t}\mathbf{a}\mathbf{n}\mathbf{}\left({\displaystyle \frac{\mathbf{5}\mathbf{\pi }}{\mathbf{2}}}\mathbf{}\mathbf{+}\mathbf{}\mathbf{x}\right)\mathbf{}\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{}\mathbf{\left(}\mathbf{4}\mathbf{\pi }\mathbf{\right)}\mathbf{}\mathbf{sec}\mathbf{\left(}\mathbf{\pi }\mathbf{\right)}}{\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{e}\mathbf{c}\mathbf{}\left({\displaystyle \frac{\mathbf{\pi }}{\mathbf{2}}}\right)\mathbf{}\mathbf{c}\mathbf{o}\mathbf{t}\mathbf{}\left({\displaystyle \frac{\mathbf{7}\mathbf{\pi }}{\mathbf{3}}}\right)\mathbf{}\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{}\left({\displaystyle \frac{\mathbf{\pi }}{\mathbf{2}}}\mathbf{}\mathbf{-}\mathbf{}\mathbf{x}\right)}\mathbf{}\mathbf{=}\mathbf{}\sqrt{\mathbf{3}}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{e}\mathit{c}\mathbf{}\mathit{x}$

Q. Prove that:
(i) $\cos \frac{2\pi }{15}\cos \frac{4\pi }{15}\cos \frac{8\pi }{15}\cos \frac{16\pi }{15}=\frac{1}{16}$

(ii) $\cos \frac{\pi }{65}\cos \frac{2\pi }{65}\cos \frac{4\pi }{65}\cos \frac{8\pi }{65}\cos \frac{16\pi }{65}\cos \frac{32\pi }{65}=\frac{1}{64}$

Q.

Find the value of cos$\frac{\pi }{6}$.cos$\frac{\pi }{3}$.cos$\frac{4\pi }{6}$.cos$\frac{8\pi }{6}$.cos$\frac{16\pi }{6}$.cos$\frac{32\pi }{6}$

1. 

2. 

3. 

4. 

Q. Solve this :
Why ?
(xi) Cosine and secant functions are even functions and all other trigonometric functions are odd functions.

Q.

Find the value of cos$\frac{\pi }{6}$.cos$\frac{\pi }{3}$.cos$\frac{4\pi }{6}$.cos$\frac{8\pi }{6}$.cos$\frac{16\pi }{6}$.cos$\frac{32\pi }{6}$

1. $\frac{\sqrt{3}}{32}$

2. $\frac{\sqrt{3}}{64}$

3. $\frac{\sqrt{3}}{8}$

4. $\frac{\sqrt{3}}{16}$

Q. Solve for x:- cot 8x . cot 3x = 1

Q. Solve this:


Use the following information to answer the next question.

A function is said to be an even function if f (-x) = f (x) and odd function if
f(-x)=-f(x)

Which of the following trigonometric functions is neither an odd function nor an even function?
(A) sin x + cos x
(B) cos x + tan²x
(C) cot x + cosec x
(D) (tan x + cot x) x cosec x

Q. cos (pie/8).cos (3 pie/8). cos (5 pie/8). cos (7 pie/8)