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第四章:部分分式 Partial Fraction

第六章:角的形成及单位 Angles and Measurements

第十三章: 方程组 Simultaneous Equations

第十五章:二元一次不等式及线性规划 linear inequality in two variables and linear programming

7.3 三角函数的诱导公式 Induced Formula of Trigonometric Functions [练习题]
7.3 三角函数的诱导公式 Induced Formula of Trigonometric Functions [练习题]
(1)
Find the value of 计算

(a)
tan43^{\circ} tan44^{\circ} tan45^{\circ} tan46^{\circ} tan47^{\circ}

(b)
sin1^{\circ}+ sin2^{\circ} + sin3^{\circ} + … + sin90^{\circ} + cos91^{\circ} + cos92^{\circ} + cos93^{\circ}+ … + cos180^{\circ}

Answer 答案:
(a) 1

(b) 0

2. Simplify 化簡
(a)
cos{(}\frac{\pi}{2}-\theta)-cos{(}\pi-\theta)+cos{(}\frac{\pi}{2}+\theta)+cos{(}\pi+\theta)
(b)
\frac{sin{(}3\pi-\theta)cot{(}-\theta-\frac{3\pi}{2})}{tan{(}\theta-5\pi)cot{(}\frac{\pi}{2}-\theta)}
(c)
\frac{sin(540°-x)cot(450°-x)cos(360°-x)}{tan(900°-x)tan(810°-x)sin(-x)}
(d)
\frac{cos( 90°+A)sec⁡(-A)tan⁡( 180°-A)}{sec⁡( 360°+A)sin⁡( 180°+A)cot⁡( 90°-A)}
(e)
sin(\pi+\theta) sec(\frac{\pi}{2}-\theta)-tan( \frac {3\pi}{2}+\theta)cot(\frac{ 3\pi}{2}-\theta)
Answer 答案:
(a) 0

(b) cos\theta

(c) sin x

(d) -1

(e) 0

(3)
In ∆ABC, prove that \frac{\sin{\left(B+C\right)\sin{\left(90^{\circ}+B\right)}}}{sin{\left(90^{\circ}-A\right)}}=\frac{\cos{\left(A+C\right)}}{\cot{\left(B+C\right)}}