About Lesson
(1) Prove that 证明
(a)
*** QuickLaTeX cannot compile formula: cosx + 2cos3x + cos5x$ = $4cos^2x\cos3x *** Error message: Unicode character 3 (U+FF13) leading text: $cosx + 2cos3
(b)
(c) =
(d) =
(e) =
(2) In triangle ABC, prove that 在三角形ABC中, 证明
(a) =
(b) =
(c) =
(3) Without using any calculator or tables, find the value of
不用计算机或查表,求下列各式的值
(a)
(b)
Answer
(a)
![Rendered by QuickLaTeX.com -\frac{1}{2}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-a8a2ca557f60ec1da4215a3607cdb1af_l3.png)
(b)
(4) If , show that
若, 试证
(5)
Prove that
. If
and
, where
and
. Find
Prove that
![Rendered by QuickLaTeX.com \frac{sin{(}A+B)-sin{(}A-B)}{cos{(}A+B)+cos{(}A-B)}=tan{B}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-a1a9dc15138dd47f76ba6a0b87dc2974_l3.png)
![Rendered by QuickLaTeX.com tan (A + B) = -\frac{5}{12}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-b274cea4e7056ed00d122fc877963314_l3.png)
![Rendered by QuickLaTeX.com tan (A - B) = \frac{3}{4}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-eaf58073c6ec3323f4fb686e9b7dfe0a_l3.png)
![Rendered by QuickLaTeX.com 0^{\circ} < A + B < 180^{\circ}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-73b3139a91c18b4707a48f04ffef1054_l3.png)
![Rendered by QuickLaTeX.com 0^{\circ} < A - B < 90^{\circ}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-8e873cf35c83150baf99f3e1e77d8a30_l3.png)
![Rendered by QuickLaTeX.com tanB](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-4396a01d12fe8f0296d05256570f3d79_l3.png)
证明 . 若
和
, 且
及
. 求
Answer
![Rendered by QuickLaTeX.com 1\frac{3}{4}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-1d42419f32d6c083f8e96bdff07c71ee_l3.png)
(6) If , prove that
=
若 , 试证
=
(7) If and
, find the value of
若 及
, 求
的值。
Answer
(8) Given that
,
, find the value of
![Rendered by QuickLaTeX.com sin x + sin y = -\frac{1}{3}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-4f3833fdc055be4f1379c8c684cca860_l3.png)
![Rendered by QuickLaTeX.com cosx + cosy = \frac{1}{2}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-f9036d565291e0ce53dcdc82ab4c7c6b_l3.png)
已知 ,
, 求下列各式的值
(a)
(b)
(c)
Answer
(a)
![Rendered by QuickLaTeX.com \frac{12}{13}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-c85d45d0fe3c78ec7c52b986a301e35f_l3.png)
(b)
(c)
(9) Find the value of
+
+
+
![Rendered by QuickLaTeX.com {cos}^4{\frac{\pi}{8}}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-f71dc90e1004474edd01f2621e00bdc9_l3.png)
![Rendered by QuickLaTeX.com {cos}^4{\frac{3\pi}{8}}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-87a0d8730b74100fa1c2b3a67dd4612c_l3.png)
![Rendered by QuickLaTeX.com {cos}^4{\frac{5\pi}{8}}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-a0c6a2a0c05a636f30d03359cf0f6189_l3.png)
![Rendered by QuickLaTeX.com {cos}^4{\frac{7\pi}{8}}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-a95f095856421b79d025ba226da36994_l3.png)
求 +
+
+
的值。
Answer
1![Rendered by QuickLaTeX.com \frac{1}{2}](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI5IiBoZWlnaHQ9IjI5IiB2aWV3Qm94PSIwIDAgOSAyOSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2VhZWFlYyIvPjwvc3ZnPg==)
![Rendered by QuickLaTeX.com \frac{1}{2}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-f5ac0f658c5eea95b9d59561e1d0ecab_l3.png)