Sách Toán – Học Toán – Đề Thi Toán

Sách Toán – Học Toán – Đề Thi Toán https://booktoan.com Học toán, Đề thi toán, Sách giáo khoa Toán, trắc nghiệm Toán online Mon, 21 Sep 2026 13:13:17 +0000 vi hourly 1 https://wordpress.org/?v=7.1.3 Tìm tập giá trị của hàm số $y = 3\sin\left(2x – \frac{\pi}{4}\right) – 1$ https://booktoan.com/tim-tap-gia-tri-cua-ham-so-y-3sinleft2x-fracpi4right-1.html https://booktoan.com/tim-tap-gia-tri-cua-ham-so-y-3sinleft2x-fracpi4right-1.html#respond Mon, 21 Sep 2026 13:13:17 +0000 https://booktoan.com/tim-tap-gia-tri-cua-ham-so-y-3sinleft2x-fracpi4right-1.html https://booktoan.com/tim-tap-gia-tri-cua-ham-so-y-3sinleft2x-fracpi4right-1.html/feed 0 Rút gọn biểu thức lượng giác $P = \frac{1 + \sin 2x – \cos 2x}{1 + \sin 2x + \cos 2x}$ https://booktoan.com/rut-gon-bieu-thuc-luong-giac-p-frac1-sin-2x-cos-2x1-sin-2x-cos-2x-2.html https://booktoan.com/rut-gon-bieu-thuc-luong-giac-p-frac1-sin-2x-cos-2x1-sin-2x-cos-2x-2.html#respond Wed, 16 Sep 2026 00:56:09 +0000 https://booktoan.com/rut-gon-bieu-thuc-luong-giac-p-frac1-sin-2x-cos-2x1-sin-2x-cos-2x-2.html https://booktoan.com/rut-gon-bieu-thuc-luong-giac-p-frac1-sin-2x-cos-2x1-sin-2x-cos-2x-2.html/feed 0 Đề bài: Chứng minh rằng: $4\sin^2\frac{a+b}{2}.\cos^2\frac{a-b}{2}+\cos2a+\cos2b\leq 2 (1)$ https://booktoan.com/de-bai-chung-minh-rang-4sin2fracab2-cos2fraca-b2cos2acos2bleq-2-1.html https://booktoan.com/de-bai-chung-minh-rang-4sin2fracab2-cos2fraca-b2cos2acos2bleq-2-1.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-chung-minh-rang-4sin2fracab2-cos2fraca-b2cos2acos2bleq-2-1.html https://booktoan.com/de-bai-chung-minh-rang-4sin2fracab2-cos2fraca-b2cos2acos2bleq-2-1.html/feed 0 Đề bài: Cho $a,b,c$ là $3$ cạnh của $\triangle ABC$.Chứng minh rằng:$a^{2}\sin^{2}x+b^{2}\cos^{2}x>c^{2}\sin^{2}x\cos^{2}x,\forall x \in R$. https://booktoan.com/de-bai-cho-abc-la-3-canh-cua-triangle-abc-chung-minh-ranga2sin2xb2cos2xc2sin2xcos2xforall-x-in-r.html https://booktoan.com/de-bai-cho-abc-la-3-canh-cua-triangle-abc-chung-minh-ranga2sin2xb2cos2xc2sin2xcos2xforall-x-in-r.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-cho-abc-la-3-canh-cua-triangle-abc-chung-minh-ranga2sin2xb2cos2xc2sin2xcos2xforall-x-in-r.html c^{2}\sin^{2}x\cos^{2}x,\forall x \in R$. Lời giải Đề bài: Cho $a,b,c$ là $3$ cạnh của $\triangle ABC$.Chứng minh rằng:$a^{2}\sin^{2}x+b^{2}\cos^{2}x>c^{2}\sin^{2}x\cos^{2}x,\forall x \in R$. Lời giải Đặt $ t=\sin^{2}{x}$.Ta có: $a^{2}\sin^{2}x+b^{2}\cos^{2}x-c^{2}\sin^{2}x\cos^{2}x$$=ta^{2}+(1-t)b^{2}-t(1-t)c^{2} $$=c^{2}t^{2}+(a^{2}-b^{2}-c^{2})t+b^{2}$Xét hàm tam thức bậc 2: $f(t)= c^{2}t^{2}+(a^{2}-b^{2}-c^{2})t+b^{2}$ có$\Delta=(a^{2}-b^{2}-c^{2})^{2}-4b^{2}c^{2}$$=(a^{2}-b^{2}-c^{2}-2bc)(a^{2}-b^{2}-c^{2}+2bc)$$=(a^{2}-(b+c)^{2})(a^{2}-(b-c)^{2})$$=-(a+b+c)(-a+b+c)(a-b+c)(a+b-c)$Vì: $\begin{cases}a+b>c \\ b+c>a \\ c+a>b \end{cases}$Do đó: $\Deltahay […]]]> https://booktoan.com/de-bai-cho-abc-la-3-canh-cua-triangle-abc-chung-minh-ranga2sin2xb2cos2xc2sin2xcos2xforall-x-in-r.html/feed 0 Đề bài: Cho $0 https://booktoan.com/de-bai-cho-0-2.html https://booktoan.com/de-bai-cho-0-2.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-cho-0-2.html https://booktoan.com/de-bai-cho-0-2.html/feed 0 Đề bài: Cho $0 https://booktoan.com/de-bai-cho-0-3.html https://booktoan.com/de-bai-cho-0-3.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-cho-0-3.html https://booktoan.com/de-bai-cho-0-3.html/feed 0 Đề bài: Cho các số $a,b,c$ thoả mãn $0 https://booktoan.com/de-bai-cho-cac-so-abc-thoa-man-0.html https://booktoan.com/de-bai-cho-cac-so-abc-thoa-man-0.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-cho-cac-so-abc-thoa-man-0.html https://booktoan.com/de-bai-cho-cac-so-abc-thoa-man-0.html/feed 0 Đề bài: Chứng minh rằng: $|a\sqrt{1-b^2}+b\sqrt{1-a^2}+\sqrt{3}[ab-\sqrt{(1-a^2)(1-b^2)}]|\leq 2$. https://booktoan.com/de-bai-chung-minh-rang-asqrt1-b2bsqrt1-a2sqrt3ab-sqrt1-a21-b2leq-2.html https://booktoan.com/de-bai-chung-minh-rang-asqrt1-b2bsqrt1-a2sqrt3ab-sqrt1-a21-b2leq-2.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-chung-minh-rang-asqrt1-b2bsqrt1-a2sqrt3ab-sqrt1-a21-b2leq-2.html https://booktoan.com/de-bai-chung-minh-rang-asqrt1-b2bsqrt1-a2sqrt3ab-sqrt1-a21-b2leq-2.html/feed 0 Đề bài: Cho $x,y$ thoả mãn $3x+4y=7$, chứng minh rằng: $x^2+y^2\geq \frac{49}{25}$. https://booktoan.com/de-bai-cho-xy-thoa-man-3x4y7-chung-minh-rang-x2y2geq-frac4925.html https://booktoan.com/de-bai-cho-xy-thoa-man-3x4y7-chung-minh-rang-x2y2geq-frac4925.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-cho-xy-thoa-man-3x4y7-chung-minh-rang-x2y2geq-frac4925.html https://booktoan.com/de-bai-cho-xy-thoa-man-3x4y7-chung-minh-rang-x2y2geq-frac4925.html/feed 0 Đề bài: Chứng minh bất dẳng thức:a) $\sin ^{4}x+\cos ^{8}x\leq 1 b) \sin^{10}x+\cos^{11}x \leq \ 1$ c)$(1+x)^{n}+(1-x)^{n} \leq 2^{n}; (|x|\leq 1), n \geq 1$ https://booktoan.com/de-bai-chung-minh-bat-dang-thuca-sin-4xcos-8xleq-1-2.html https://booktoan.com/de-bai-chung-minh-bat-dang-thuca-sin-4xcos-8xleq-1-2.html#respond Sat, 10 Jul 2021 17:00:00 +0000 https://booktoan.com/de-bai-chung-minh-bat-dang-thuca-sin-4xcos-8xleq-1-2.html https://booktoan.com/de-bai-chung-minh-bat-dang-thuca-sin-4xcos-8xleq-1-2.html/feed 0