\(90^0< a< 180^0\)

=>\(cosa< 0\)

\(sin^2a+cos^2a=1\)

=>\(cos^2a+\dfrac{9}{25}=1\)

=>\(cos^2a=1-\dfrac{9}{25}=\dfrac{16}{25}\)

mà cosa<0

nên \(cosa=-\dfrac{4}{5}\)

\(tana=\dfrac{sina}{cosa}=\dfrac{3}{5}:\dfrac{-4}{5}=-\dfrac{3}{4}\)

\(A=2\cdot cos^2a-5\cdot tan^2a\)

\(=2\cdot\left(-\dfrac{4}{5}\right)^2-5\cdot\left(-\dfrac{3}{4}\right)^2\)

\(=2\cdot\dfrac{16}{25}-5\cdot\dfrac{9}{16}\)

\(=\dfrac{32}{25}-\dfrac{45}{16}=\dfrac{-613}{400}\)

sin/ cos = tan 
từ đó tự làm nhé

a: 

b: \(B=3-sin^290^0+2\cdot cos^260^0-3\cdot tan^245^0\)

\(=3-1+2\cdot\left(\dfrac{1}{2}\right)^2-3\cdot1^2\)

\(=2-3+2\cdot\dfrac{1}{4}=-1+\dfrac{1}{2}=-\dfrac{1}{2}\)

c: \(C=sin^245^0-2\cdot sin^250^0+3\cdot cos^245^0-2\cdot sin^240^0+4\cdot tan55\cdot tan35\)

\(=\left(\dfrac{\sqrt{2}}{2}\right)^2+3\cdot\left(\dfrac{\sqrt{2}}{2}\right)^2-2\cdot\left(sin^250^0+sin^240^0\right)+4\)

\(=\dfrac{1}{2}+3\cdot\dfrac{1}{2}-2+4\)

\(=2-2+4=4\)

Lời giải:

$\cos a=\sqrt{1-\sin ^2a}=\frac{4}{5}$

$\tan a=\frac{\sin a}{\cos a}=\frac{3}{5}: \frac{4}{5}=\frac{3}{4}$

$A=2\tan a+\cos a=2.\frac{3}{4}+\frac{4}{5}=\frac{23}{10}$

mình ko bt cách viết  phân số nên đường gạch ngang mờ mờ mà các bạn nhìn là phân số nhé

Lời giải:

a. 

\(A=\frac{3}{2}-2(\frac{\cos x}{\sin x})^2=\frac{3}{2}-2.(\frac{1}{\tan x})^2=\frac{3}{2}-\frac{1}{2}(\frac{-3}{2})^2=-3\)

b.

\(A=\frac{1}{2}(\frac{\sin x}{\cos x})^2-\frac{5}{2}=2(\frac{1}{\cot x})^2-\frac{5}{2}=2(\frac{5}{3})^2-\frac{5}{2}=\frac{55}{18}\)

a, \(A=\dfrac{3sin^2\left(x\right)-cos^2\left(x\right)}{2sin^2\left(x\right)}=\dfrac{3}{2}-\dfrac{1}{2}\dfrac{cos^2\left(x\right)}{sin^2\left(x\right)}=\dfrac{3}{2}-\dfrac{1}{2}\cdot\dfrac{1}{tan^2\left(x\right)}=\dfrac{3}{2}-\dfrac{1}{2}\cdot\left(-\dfrac{3}{2}\right)^2=-3\)

b, \(A=\dfrac{sin^2\left(x\right)-5cos^2\left(x\right)}{2cos^2\left(x\right)}=\dfrac{1}{2}\dfrac{sin^2\left(x\right)}{cos^2\left(x\right)}-\dfrac{5}{2}=\dfrac{1}{2}\cdot\dfrac{1}{cot^2\left(x\right)}-\dfrac{5}{2}=\dfrac{1}{2}\cdot\left(\dfrac{5}{3}\right)^2-\dfrac{5}{2}=\dfrac{55}{18}\)

\(A=\left(\dfrac{1-cos2x}{2}\right)^2+2\left(\dfrac{1+cos2x}{2}\right)^2\)

\(=\dfrac{3}{4}cos^22x+\dfrac{1}{2}cos2x+\dfrac{3}{4}\)

\(A=\dfrac{1}{12}\left(3cos2x+1\right)^2+\dfrac{2}{3}\ge\dfrac{2}{3}\)

\(A_{min}=\dfrac{2}{3}\) khi \(cos2x=-\dfrac{1}{3}\)

\(A=\dfrac{3cos^22x+2cos2x-5}{4}+2=\dfrac{\left(3cos2x+5\right)\left(cos2x-1\right)}{4}+2\le2\)

\(A_{max}=2\) khi \(cos2x=1\)

1.

a) \(\left(1-cos_x\right)\left(1+cos_x\right)-sin^2_x=1-cos^2_x-sin^2_x=1-\left(cos^2_x+sin^2_x\right)=1-1=0\)

b) \(tan^2_x\left(2.cos^2_x+sin^2_x-1\right)+cos^2_x=tan^2_x\left(cos^2_x+sin^2_x+cos^2_x-1\right)+cos^2_x=tan^2_x\left(1-1+cos^2_x\right)+cos^2_x=tan^2_x.cos^2_x+cos^2_x=\left(tan_x.cos_x\right)^2+cos^2_x=sin^2_x+cos^2_x=1\)2. Ta có \(9>5\Leftrightarrow\sqrt{9}>\sqrt{5}\Leftrightarrow3>\sqrt{5}\Leftrightarrow3-\sqrt{5}>0\)

Vậy \(3-\sqrt{5}>0\)