lượng giác 10 đây

Question

1. Chứng minh các biểu thức sau:

a.$\frac{2sina - sin2a}{2sina +sin2a}$ = $tan^{2}$$\frac{a}{2}$.

b.(sina + sinb)$^{2}$ + (cosa + cosb)$^{2}$ = 4cos$^{2}$$\frac{a + b}{2}$.

khangnguyenthanh · Answer 1 · 4/30/2013 8:28:11 PM

b. Ta có:

$(\sin a+\sin b)^2+(\cos a+\cos b)^2$

$=\sin^2 a+2\sin a\sin b+\sin^2b+\cos^2a+2\cos a\cos b+\cos^2b$

$=2+2(\sin a\sin b+\cos a\cos b)$

$=2+2\cos(a-b)$

$=4\cos^2\dfrac{a-b}{2}$

Trả lời 30-04-13 08:28 PM

khangnguyenthanh
72K 2 480 42

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khangnguyenthanh · Answer 2 · 4/30/2013 8:23:50 PM

a. Ta có:

$\dfrac{2\sin a-\sin2a}{2\sin a+\sin2a}$

$=\dfrac{2\sin a-2\sin a\cos a}{2\sin a+2\sin a\cos a}$

$=\dfrac{1-\cos a}{1+\cos a}$

$=\dfrac{\sin^2\dfrac{a}{2}}{\cos^2\dfrac{a}{2}}=\tan^2\dfrac{a}{2}$

Trả lời 30-04-13 08:23 PM

khangnguyenthanh
72K 2 480 42

332K 4M

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