Quiz about Công thức toán

Question 1

cos(a-b) = ?

Accepted Answer

cosa.cosb+sina.sinb

Answer

cosa.cosb-sina.sinb

Answer

sina.cosb-cosa.sinb

Answer

sina.cosb+cosa.sinb

Question 2

cos(a + b)=?

Accepted Answer

cosa.cosb-sina.sinb

Answer

cosa.cosb+sina.sinb

Answer

sina.cosb+sinb.cosa

Answer

sina.cosb-sinb.cosa

Question 3

sin(a-b)=?

Accepted Answer

sina.cosb - cosa.sinb

Answer

cos(a - b)

Answer

cos(a)cos(b) + sin(a)sin(b)

Answer

sin(a) + sin(b)

Question 4

tan(a+b)=?

Accepted Answer

$$\frac{\left( an a+ an b ight)}{1- an a. an b}$$

Answer

tan(a) - tan(b)

Answer

tan(a + b)

Answer

$$\frac{\left( an a+ an b ight)}{1+ an a. an b}$$

Question 5

tan(a-b)=?

Accepted Answer

$$\frac{\left( an a- an b ight)}{1+ an a. an b}$$

Answer

$$\frac{\left( an a- an b ight)}{1- an a. an b}$$

Answer

tan(a - b)

Answer

tan(a)tan(b)

Question 6

sin2a=?

Accepted Answer

sin(2a) = $$2.\sin a.\cos a$$

Answer

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

Answer

sin(2a) = $$\frac{\sin a}{\cos a}$$

Answer

sin(2a) = $$2\sin^{2\ }a$$

Question 7

$$\sin^2a=?$$

Accepted Answer

$$\frac{1-\cos2a}{2}$$

Answer

$$\frac{1+\cos2a}{2}$$

Answer

$$\frac{1}{\cos2a}$$

Answer

$$\frac{1}{ an2a}$$

Question 8

$$\cos^2a$$ =?

Accepted Answer

$$\frac{1+\cos2a}{2}$$

Answer

$$\frac{1-\cos2a}{2}$$

Answer

$$\frac{1+\cos a}{2}$$

Answer

$$1+\cos2a$$

Question 9

$$ an2a=?$$

Accepted Answer

$$\frac{2 an a}{1- an^2a}$$

Answer

$$\frac{ an a}{1- an^2a}$$

Answer

$$\frac{2 an a}{1+ an^2a}$$

Answer

$$\frac{ an a}{1+ an^2a}$$

Question 10

$$\cos a.\cos b=?$$

Accepted Answer

$$\frac{1}{2}\left[\cos\left(a+b\right)+\cos\left(a-b\right)\right]$$

Answer

$$\frac{1}{2}\left[\cos\left(a+b\right)-\cos\left(a-b\right)\right]$$

Answer

$$\frac{1}{2}\left[\sin\left(a+b\right)+\cos\left(a-b\right)\right]$$

Answer

$$\frac{1}{2}\left[\sin\left(a+b\right)+\sin\left(a-b\right)\right]$$

Question 11

$$\sin a.\sin b$$ =?

Accepted Answer

$$\frac{1}{2}\cos\left[\left(a-b\right)-\cos\left(a+b\right)\right]$$

Answer

$$\frac{1}{2}\cos\left[\left(a-b\right)+\cos\left(a+b\right)\right]$$

Answer

$$\frac{1}{-2}\cos\left[\left(a+b\right)+\cos\left(a+b\right)\right]$$

Answer

$$-\frac{1}{2}\cos\left[\left(a+b\right)-\cos\left(a-b\right)\right]$$

Answer

$$\cos\left[\left(a-b\right)-\cos\left(a+b\right)\right]$$

Question 12

$$\sin a.\cos b=?$$

Accepted Answer

$$\frac{1}{2}\sin\left[\left(a+b\right)+\sin\left(a-b\right)\right]$$

Answer

$$\frac{1}{2}\sin\left[\left(a+b\right)-\sin\left(a-b\right)\right]$$

Answer

$$\frac{1}{2}\sin\left[\left(a-b\right)+\sin\left(a-b\right)\right]$$

Answer

$$\sin\left[\left(a+b\right)+\sin\left(a-b\right)\right]$$

Question 13

$$\cos a+\cos b=?$$

Accepted Answer

$$2\cos\left(\frac{a+b}{2}\right).\cos\left(\frac{a-b}{2}\right)$$

Answer

$$2\sin\left(\frac{a+b}{2}\right).\cos\left(\frac{a-b}{2}\right)$$

Answer

$$\sin\left(\frac{a+b}{2}\right).\sin\left(\frac{a-b}{2}\right)$$

Answer

$$2 an\left(\frac{a+b}{2} ight).\cos\left(\frac{a-b}{2} ight)$$

Question 14

$$\cos a-\cos b=?$$

Accepted Answer

$$-2\sin\left(\frac{a+b}{2}\right).\sin\left(\frac{a-b}{2}\right)$$

Answer

$$2\sin\left(\frac{a+b}{2}\right).\sin\left(\frac{a-b}{2}\right)$$

Answer

$$-2\cos\left(\frac{a+b}{2}\right).\sin\left(\frac{a-b}{2}\right)$$

Answer

$$-2\cot\left(\frac{a+b}{2}\right).\sin\left(\frac{a-b}{2}\right)$$

Question 15

$$\sin a+\sin b=?$$

Accepted Answer

$$2\sin\left(\frac{a+b}{2}\right).\cos\left(\frac{a-b}{2}\right)$$

Answer

$$-2\cos\left(\frac{a+b}{2}\right).\sin\left(\frac{a-b}{2}\right)$$

Answer

$$2\sin\left(\frac{a+b}{2}\right).\sin\left(\frac{a-b}{2}\right)$$

Answer

$$-2\sin\left(\frac{a+b}{2}\right).\cos\left(\frac{a-b}{2}\right)$$

Question 16

$$\sin a-\sin b=?$$

Accepted Answer

$$2\cos\left(\frac{a+b}{2}\right).\sin\left(\frac{a-b}{2}\right)$$

Answer

$$-2\sin\left(\frac{a+b}{2}\right).\sin\left(\frac{a-b}{2}\right)$$

Answer

$$-2\cos\left(\frac{a+b}{2}\right).\sin\left(\frac{a-b}{2}\right)$$

Answer

$$\cos\left(\frac{a+b}{2}\right).\sin\left(\frac{a-b}{2}\right)$$

Question 17

$$\sin x=-1\ \leftrightarrow\ x=?$$

Accepted Answer

$$-\frac{\pi}{2}+k2\pi$$

Answer

$$\frac{\pi}{2}+k2\pi$$

Answer

$$-\frac{\pi}{2}+k\pi$$

Answer

$$-\frac{\pi}{2}+k4\pi$$

Question 18

$$\sin x=0\ \leftrightarrow\ x=?$$

Accepted Answer

$$k\pi$$

Answer

$$-\frac{\pi}{2}+k2\pi$$

Answer

$$\pi+k2\pi$$

Answer

$$k\pi-\pi$$

Question 19

$$\sin x=1\ \leftrightarrow\ x=?$$

Accepted Answer

$$x=\frac{\pi}{2}+k2\pi$$

Answer

$$x=-\frac{\pi}{2}+k2\pi$$

Answer

$$x=-\frac{\pi}{2}-k2\pi$$

Answer

$$x=\frac{\pi}{2}+k\pi$$

Question 20

$$\cos x=-1\ \leftrightarrow\ x=?$$

Accepted Answer

$$\pi+k2\pi$$

Answer

$$\frac{\pi}{2}+k2\pi$$

Answer

$$2\pi+k2\pi$$

Answer

$$\pi-k2\pi$$

Question 21

$$\cos x=0\ \leftrightarrow\ x=?$$

Accepted Answer

$$k\pi$$

Answer

$$\frac{\pi}{2}+k\pi$$

Answer

$$\pi+k\pi$$

Answer

$$k2\pi$$

Question 22

$$\cos x=1\ \leftrightarrow\ x=?$$

Accepted Answer

$$x=k2\pi$$

Answer

$$\ x=\frac{\pi}{2}+k\pi$$

Answer

$$\ x=\frac{\pi}{2}-k\pi$$

Answer

$$\ x=\frac{\pi}{2}+k2\pi$$

Question 23

$$ an x=-1\ \leftrightarrow\ x=?$$

Accepted Answer

$$-\frac{\pi}{4}+k\pi$$

Answer

$$\frac{\pi}{4}+k\pi$$

Answer

$$-\frac{\pi}{2}+k\pi$$

Answer

$$k\pi$$

Question 24

$$ an x=0\ \leftrightarrow\ x=?$$

Accepted Answer

$$x=k\pi$$

Answer

$$x=-\frac{\pi}{4}+k\pi$$

Answer

$$x=\frac{\pi}{4}+k\pi$$

Answer

$$k2\pi$$

Question 25

$$ an x=1\ \leftrightarrow\ x=?$$

Accepted Answer

$$\frac{\pi}{4}+k\pi$$

Answer

$$\frac{-\pi}{2}+k\pi$$

Answer

$$-\frac{\pi}{4}+k\pi$$

Answer

$$k\pi$$

Question 26

$$\cot x=-1\ \leftrightarrow\ x=?$$

Accepted Answer

$$-\frac{\pi}{4}+k\pi$$

Answer

$$\frac{\pi}{2}+k\pi$$

Answer

$$\frac{\pi}{4}+k\pi$$

Answer

$$\frac{\pi}{2}+k2\pi$$

Question 27

$$\cot x=0\ \leftrightarrow\ x=?$$

Accepted Answer

$$\frac{\pi}{2}+k\pi$$

Answer

$$-\frac{\pi}{4}+k\pi$$

Answer

$$\frac{\pi}{4}+k\pi$$

Answer

$$-\frac{\pi}{2}+k\pi$$

Question 28

$$\cot\ x=1\ \leftrightarrow\ x=?$$

Accepted Answer

$$\frac{\pi}{4}+k\pi$$

Answer

$$\frac{\pi}{2}+k\pi$$

Answer

$$-\frac{\pi}{4}+k\pi$$

Answer

$$\pi+k\pi$$

Question 29

$$\cos\left(-a\right)=?$$

Accepted Answer

$$\cos a$$

Answer

$$-\cos a$$

Answer

$$\sin a$$

Answer

$$	an a$$

Question 30

$$\sin\left(-a\right)=?$$

Accepted Answer

$$-\sin a$$

Answer

$$\sin a$$

Answer

$$\cos a$$

Answer

$$	an a$$

Question 31

$$ an\left(-a ight)=?$$

Accepted Answer

$$-	an a$$

Answer

$$	an a$$

Answer

$$\cot a$$

Answer

$$-\cot a$$

Question 32

$$\cot\left(-a\right)=?$$

Accepted Answer

$$-\cot a$$

Answer

$$\cot a$$

Answer

$$\sin a$$

Answer

$$-	an a$$

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