- A$3 sec^2 3x tan x \,\, tan 2x + sec^2 x tan 2x\,\, tan 3x + 2 sec^2 2x\,\, tan 3x \,\,tan x$
- B$2y (cosec 2x + 2 cosec 4x + 3 cosec 6x)$
- C$3 sec^2 3x - 2 sec^2 2x -sec^2 x$
- ✓All of the above
$\tan 3 x=\frac{\tan 2 x+\tan x}{1-\tan x \tan 2 x}$
$\tan 3 x-\tan x \tan 2 x \tan 3 x=\tan x+\tan 2x$
$y=\operatorname{tan} 3 x-\operatorname{tan} x-\operatorname{tan} 2 x$
$\frac{d y}{d x}=3 \sec ^{2} 3 x-\sec ^{2} x-2 \operatorname{sec}^{2} 2 x$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$1.$ If $\mathrm{f}(-10 \sqrt{2})=2 \sqrt{2}$, then $\mathrm{f}^{\prime \prime}(-10 \sqrt{2})=$
$(A)$ $\frac{4 \sqrt{2}}{7^3 3^2}$ $(B)$ $-\frac{4 \sqrt{2}}{7^3 3^2}$ $(C)$ $\frac{4 \sqrt{2}}{7^3 3}$ $(D)$ $-\frac{4 \sqrt{2}}{7^3 3}$
$2.$ The area of the region bounded by the curves $y=f(x)$, the $x$-axis, and the lines $x=a$ and $x=b$, where $-\infty < \mathrm{a} < \mathrm{b} < -2$, is
$(A)$ $\int_a^b \frac{x}{3\left((f(x))^2-1\right)} d x+b f(b)-a f(a)$
$(B)$ $-\int_a^b \frac{x}{3\left((f(x))^2-1\right)} d x+b f(b)-a f(a)$
$(C)$ $\int_a^b \frac{x}{3\left((f(x))^2-1\right)} d x-b f(b)+a f(a)$
$(D)$ $-\int_a^b \frac{x}{3\left((f(x))^2-1\right)} d x-b f(b)+a f(a)$
$3.$ $\int_{-1}^1 g^{\prime}(x) d x=$
$(A)$ $2 g(-1)$ $(B)$ 0 $(C)$ $-2 g(1)$ $(D)$ $2 \mathrm{~g}(1)$
Give the answer question $1,2$ and $3.$