Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(A=tan18^otan288+sin32^osin148^o-sin302^osin122^o\)
\(=tan18^o.tan\left(-72^o\right)+sin32^o.sin32^o+sin58^o.sin58^o\)
\(=-tan18^o.cot18^o+sin^232^o+sin^258^o\)
\(=-1+sin^232^o+cos^232^2=-1+1=0\).
b) \(B=\dfrac{1+sin^4\alpha-cos^4\alpha}{1-sin^6\alpha-cos^6\alpha}\)
\(=\dfrac{1+\left(sin^2\alpha+cos^2\alpha\right)\left(sin^2\alpha-cos^2\alpha\right)}{1-\left(sin^6\alpha+cos^6\alpha\right)}\)
\(=\dfrac{1+sin^2\alpha-cos^2\alpha}{1-\left(sin^2\alpha+cos^2\alpha\right)\left(sin^2\alpha-sin\alpha cos\alpha+cos^2\alpha\right)}\)
\(=\dfrac{sin^2\alpha+1-cos^2\alpha}{1-\left(1-sin\alpha.cos\alpha\right)}\)
\(=\dfrac{sin^2\alpha+sin^2\alpha}{sin\alpha cos\alpha}\)
\(=\dfrac{2sin^2\alpha}{sin\alpha cos\alpha}=\dfrac{2sin\alpha}{cos\alpha}=2tan\alpha\).
a)\(sin^2\left(180^o-\alpha\right)+tan^2\left(180-\alpha\right).tan^2\left(270^o+\alpha\right)\)\(+sin\left(90^o+\alpha\right)cos\left(\alpha-360^o\right)\)
\(=sin^2\alpha+tan^2\alpha.cot^2\alpha+cos\alpha cos\alpha\)
\(=sin^2\alpha+cos^2\alpha+\left(tan\alpha cot\alpha\right)^2=1+1=2\).
\(\dfrac{cos\left(\alpha-180^o\right)}{sin\left(180^o-\alpha\right)}+\dfrac{tan\left(\alpha-180^o\right)cos\left(180^o+\alpha\right)sin\left(270^o+\alpha\right)}{tan\left(270^o+\alpha\right)}\)
\(=\dfrac{cos\left(180^o-\alpha\right)}{sin\left(180^o-\alpha\right)}+\dfrac{-tan\left(180^o-\alpha\right).cos\alpha.sin\left(90^o+\alpha\right)}{-tan\left(90^o+\alpha\right)}\)
\(=tan\left(180^o-\alpha\right)+\dfrac{tan\alpha.cos\alpha.cos\alpha}{cot\alpha}\)
\(=-tan\alpha+tan^2\alpha cos^2\alpha\)
\(=tan\alpha\left(-1+tan\alpha cos^2\alpha\right)\)
\(=tan\alpha\left(sin\alpha cos\alpha-1\right)\).
a) \(sin20^o+2sin40^o-sin100^o=sin20^o-sin100^o+2sin40^o\)
\(=2cos60^osin\left(-40^o\right)+2sin40^o\)\(=-2cos60^osin40^o+2sin40^o\)
\(=2sin40^o\left(-cos60^o+1\right)=2sin40^o.\left(-\dfrac{1}{2}+1\right)=sin40^o\)(đpcm).
b) \(\dfrac{sin\left(45^o+\alpha\right)-cos\left(45^o+\alpha\right)}{sin\left(45^o+\alpha\right)+cos\left(45^o+\alpha\right)}\)
\(=\dfrac{sin\left(45^o+\alpha\right)-sin\left(45^o-\alpha\right)}{sin\left(45^o+\alpha\right)+sin\left(45^o-\alpha\right)}=\dfrac{2cos45^o.sin\alpha}{2sin45^o.cos\alpha}\)
\(=tan\alpha\) (Đpcm).
a) \(0< \alpha< 90^o\)
b) \(90^o< \alpha< 180^o\)
c) \(0< \alpha< 90^o\)
d) \(90^o< \alpha< 180^o\)
a) \(sin\left(270^o-\alpha\right)=sin\left(-90^o-\alpha\right)=-sin\left(90^o+\alpha\right)\)\(=-cos\alpha\).
b) \(cos\left(270^o-\alpha\right)=cos\left(-90^o-\alpha\right)=cos\left(90^o+\alpha\right)\)\(=-sin\alpha\).
c) \(sin\left(270^o+\alpha\right)=sin\left(-90^o+\alpha\right)=-sin\left(90^o-\alpha\right)\)\(=-cos\alpha\).
d) \(cos\left(270^o+\alpha\right)=cos\left(-90^o+\alpha\right)=cos\left(90^o-\alpha\right)\)\(=sin\alpha\).
a) Tồn tại do \(\left|sin\alpha\right|\le1\).
b) Tồn tại do \(\left|cos\alpha\right|\le1\).
c) Tồn tại do\(\left|sin\alpha\right|\le1\).
d) Không tồn tại do \(\left|cos\alpha\right|\ge1\).
e) Không tồn tại do \(\left|sin\alpha\right|\ge1\).
g) Không tồn tại do \(\left|cos\alpha\right|\ge1\).
a) \(\dfrac{\sin2\text{a}+\cos a}{1+\cos2\text{a}+\cos a}=2\tan a\)
a) \(\dfrac{sin2\alpha+sin\alpha}{1+cos2\alpha+cos\alpha}=\dfrac{2sin\alpha cos\alpha+sin\alpha}{2cos^2\alpha+cos\alpha}\)\(=\dfrac{sin\alpha\left(2cos\alpha+1\right)}{cos\alpha\left(2cos\alpha+1\right)}=\dfrac{sin\alpha}{cos\alpha}=tan\alpha\).
\(\sin\alpha=\dfrac{2\sqrt{2}}{3};\cos\alpha=\dfrac{1}{3}\)
a) Do \(90^o< \alpha< 180^o\) nên \(sin\alpha>0;cos\alpha< 0\).
b) Do \(180^o< \alpha< 270^o\) nên \(sin\alpha< 0;cos\alpha< 0\).
c) Do \(270^o< \alpha< 360^o\) nên \(sin\alpha< 0;cos\alpha>0\).
d) \(\alpha=1280^o=3.360^o+200^o\)
\(sin1280^o=sin\left(3.360^o+200^o\right)=sin200^o< 0\).
e)
\(sin\left(-235^o\right)=sin\left(-235^o+360^o\right)=sin125^o>0\).
\(cos\left(-235^o\right)=cos\left(-235^o+360^o\right)=cos125^o< 0\).
d) \(sin\left(-1876\right)=sin\left(-1876^o+1800^o\right)=sin\left(-76^o\right)\)\(=-sin76^o< 0\).
\(cos\left(-1876^o\right)=cos\left(-76^o\right)=cos76^o>0\).