4b.

\(\dfrac{\pi}{2}< a< \pi\Rightarrow cosa< 0\Rightarrow cosa=-\sqrt{1-sin^2a}=-\dfrac{4}{5}\)

\(\Rightarrow tana=\dfrac{sina}{cosa}=-\dfrac{3}{4}\)

\(tan\left(a+\dfrac{\pi}{3}\right)=\dfrac{tana+tan\left(\dfrac{\pi}{3}\right)}{1-tana.tan\left(\dfrac{\pi}{3}\right)}=\dfrac{-\dfrac{3}{4}+\sqrt{3}}{1-\left(-\dfrac{3}{4}\right).\sqrt{3}}=...\)

c.

\(\dfrac{3\pi}{2}< a< 2\pi\Rightarrow cosa>0\Rightarrow cosa=\sqrt{1-sin^2a}=\dfrac{5}{13}\)

\(cos\left(\dfrac{\pi}{3}-a\right)=cos\left(\dfrac{\pi}{3}\right).cosa+sin\left(\dfrac{\pi}{3}\right).sina=\dfrac{1}{2}.\dfrac{5}{13}+\left(-\dfrac{12}{13}\right).\dfrac{\sqrt{3}}{2}=...\)

Bán kính hình tròn:
\(18,84:3,14:2=3\left(cm\right)\)
Diện tích hình tròn:
\(3\times3\times3,14=28,26\left(cm^2\right)\)
Đường kính hình tròn:
\(3\times2=6\left(cm\right)\)
Diện tích hình thoi:
\(\dfrac{6\times6}{2}=18\left(cm^2\right)\)
Diện tích phần gạch chéo:
\(28,26-18=10,26\left(cm^2\right)\)

4:

a: -90<a<0

=>cos a>0

cos^2a=1-(-4/5)^2=9/25

=>cosa=3/5

\(sin\left(45-a\right)=sin45\cdot cosa-cos45\cdot sina=\dfrac{\sqrt{2}}{2}\left(cosa-sina\right)\)

\(=\dfrac{\sqrt{2}}{2}\left(\dfrac{3}{5}-\dfrac{4}{5}\right)=\dfrac{-\sqrt{2}}{10}\)

b: pi/2<a<pi

=>cosa<0

cos^2a+sin^2a=0

=>cos^2a=16/25

=>cosa=-4/5

tan a=3/5:(-4/5)=-3/4

\(tan\left(a+\dfrac{pi}{3}\right)=\dfrac{tana+\dfrac{tanpi}{3}}{1-tana\cdot tan\left(\dfrac{pi}{3}\right)}\)

\(=\dfrac{-\dfrac{3}{4}+\sqrt{3}}{1-\dfrac{-3}{4}\cdot\sqrt{3}}=\dfrac{48-25\sqrt{3}}{11}\)

c: 3/2pi<a<pi

=>cosa>0

cos^2a+sin^2a=1

=>cos^2a=25/169

=>cosa=5/13

cos(pi/3-a)

\(=cos\left(\dfrac{pi}{3}\right)\cdot cosa+sin\left(\dfrac{pi}{3}\right)\cdot sina\)

\(=\dfrac{5}{13}\cdot\dfrac{1}{2}+\dfrac{-12}{13}\cdot\dfrac{\sqrt{3}}{2}=\dfrac{5-12\sqrt{3}}{26}\)

5:

a: sin x=2*cosx

\(A=\dfrac{6cosx+2cosx-4\cdot8\cdot cos^3x}{cos^3x-2cosx}\)

\(=\dfrac{8-32cos^2x}{cos^2x-2}\)

b: VT=sin^4(pi/2-x)+cos^4(x+pi/2)+6*1/2*sin^22x+1/2*cos4x

=cos^4x+sin^4x+3*sin^2(2x)+1/2*(1-2*sin^2(2x))

=1-2*sin^2x*cos^2x+3*sin^2(2x)+1/2-sin^2(2x)

==3/2=VP

Xét BPT: \(x^2-8x+15\le0\Leftrightarrow3\le x\le5\Rightarrow D_1=\left[3;5\right]\)

Xét BPT: \(\left(m^2+1\right)x+m\ge23+2mx\)

\(\Leftrightarrow\left(m^2-2m+1\right)x\ge23-m\)

\(\Leftrightarrow\left(m-1\right)^2x\ge23-m\) (1)

- Với \(m=1\Rightarrow\left(1\right)\) trở thành \(0\ge22\) (vô lý) \(\Rightarrow\left(1\right)\) vô nghiệm (loại)

- Với \(m\ne1\Rightarrow\left(m-1\right)^2>0;\forall m\)

\(\left(1\right)\Leftrightarrow x\ge\dfrac{23-m}{\left(m-1\right)^2}\) \(\Rightarrow D_2=\left[\dfrac{23-m}{(m-1)^2};+\infty \right)\)

Hệ đã cho có nghiệm khi và chỉ khi \(D_1\cap D_2\ne\varnothing\)

\(\Rightarrow\dfrac{23-m}{\left(m-1\right)^2}\le5\)

\(\Leftrightarrow23-m\le5\left(m-1\right)^2\)

\(\Leftrightarrow5m^2-9m-18\ge0\Rightarrow\left[{}\begin{matrix}m\ge3\\m\le-\dfrac{6}{5}\end{matrix}\right.\)

a. x² - 2x

⇔ x(x - 2)

b. 3x - 6y

⇔ 3(x - 2y)

c. 5(x + 3y) - 15x(x + 3y)

⇔ (5 - 15x)(x + 3y)

d. 3(x - y) - 5x(y - x)

⇔ 3(x - y) + 5x(x - y)

⇔ (3 + 5x)(x - y)

#include <bits/stdc++.h>

using namespace std;

double a,b;

int main()

{

cin>>a>>b;

cout<<(a+b)*2;

return 0;

}