Sum and difference identities Quiz 1

Question 1

Solve $$-\cos x\sin x-{{\sin }^{2}}x=3.$$

Accepted Answer

$$\cot x+4+3\cot {{\left( x \right)}^{2}}=0$$

Answer

$$\cot x-4-3\cot {{\left( x \right)}^{2}}=0$$

Answer

$$-\cot x-4+3\cot {{\left( x \right)}^{2}}=0$$

Answer

$$-\cot x-4-3\cot {{\left( x \right)}^{2}}=0$$

Question 2

Solve $${{\sin }^{2}}x+\cos x=1+\sin x\cot x.$$

Accepted Answer

$${{\sin }^{2}}x=	ext{L}$$

Answer

$$\cos 2x=	ext{L}$$

Answer

$$\cos x=	ext{L}$$

Answer

$$\cos 2x=-	ext{L}$$

Question 3

If $$	an \beta =\dfrac{\sin \alpha -\sin r}{\cos r-\cos \alpha },$$ which of the following is true?

Accepted Answer

$$2\beta =\alpha +r$$

Answer

$$\dfrac{2\beta }{\alpha +r}$$

Answer

$$\dfrac{2\beta }{\alpha -r}$$

Answer

$$2\beta =\alpha -r$$

Question 4

Solve the equation $$3{{\cos }^{2}}x-10\sin x+9=0$$

Accepted Answer

$$\sin \left( x \right)=\dfrac{-5+\sqrt{61}}{3},\sin \left( x \right)=\dfrac{-5-\sqrt{61}}{3}$$

Answer

$$\sin \left( x \right)=\dfrac{+5+\sqrt{61}}{3},\sin x=\dfrac{-5-\sqrt{61}}{3}$$

Answer

$$\sin \left( x \right)=\dfrac{5-\sqrt{61}}{3},\sin \left( x \right)=\dfrac{5+\sqrt{61}}{3}$$

Answer

$$\sin \left( x \right)=\dfrac{+5-\sqrt{61}}{3},\sin \left( x \right)=\dfrac{-5+\sqrt{61}}{3}$$

Question 5

Solve this equation $$\sin \dfrac{x}{3}-4{{\cos }^{2}}\dfrac{x}{3}=0.$$

Accepted Answer

$$\sin \dfrac{x}{3}=\dfrac{-1+\sqrt{65}}{8},\dfrac{-1-\sqrt{65}}{8}$$

Answer

$$\sin \dfrac{x}{3}=\dfrac{-1+\sqrt{65}}{8},\dfrac{+1+\sqrt{65}}{8}$$

Answer

$$\sin \dfrac{x}{3}=\dfrac{1-\sqrt{65}}{8},\dfrac{-1-\sqrt{65}}{8}$$

Answer

$$\sin \dfrac{x}{3}=\dfrac{-1+\sqrt{65}}{8},\dfrac{-1+\sqrt{65}}{8}$$