7.3 三角函数的诱导公式 Induced Formula of Trigonometric Functions [练习题] - 独中课程 | 线上补习

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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)

*** QuickLaTeX cannot compile formula:
\frac{sin(540°-x)cot(450°-x)cos(360°-x)}{tan(900°-x)tan(810°-x)sin(-x)}

*** Error message:
Package inputenc Error: Unicode character ° (U+00B0)
leading text: ...(360°-x)}{tan(900°-x)tan(810°-x)sin(-x)}

(d)

*** QuickLaTeX cannot compile formula:
\frac{cos( 90°+A)sec⁡(-A)tan⁡( 180°-A)}{sec⁡( 360°+A)sin⁡( 180°+A)cot⁡( 90°-A)}

*** Error message:
Package inputenc Error: Unicode character ° (U+00B0)
leading text: ...( 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) $cos\theta$

(d) $-1$

(e) $0$

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

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