Double-angle identity Quiz 1

Question 1

Calculate the value of $$\cos {{150}^{\circ }}$$ if $$\cos {{75}^{\circ }}=\dfrac{\sqrt{3}-1}{2\sqrt{2}}$$

Accepted Answer

$$\dfrac{-\sqrt{3}}{2}$$

Answer

$$\dfrac{\sqrt{3}}{2}$$

Answer

$$\dfrac{1}{2}$$

Answer

$$\dfrac{-1}{2}$$

Question 2

Calculate the value of $$\dfrac{1+\cos 4	heta }{1-\cos 4	heta }$$ if $$	an 2	heta =\sqrt{3}$$

Accepted Answer

$$\dfrac{1}{3}$$

Answer

$$\dfrac{1}{\sqrt{3}}$$

Answer

$$\sqrt{3}$$

Answer

$$3$$

Question 3

Calculate the value of $$\dfrac{\sin 2	heta }{1-\cos 2	heta }$$ if value of $$\sin 	heta =\dfrac{3}{5}$$ in first quadrant.

Accepted Answer

$$\dfrac{4}{3}$$

Answer

$$\dfrac{3}{5}$$

Answer

$$\dfrac{4}{5}$$

Answer

$$\dfrac{3}{4}$$

Question 4

Calculate the value of $$\dfrac{\sin \dfrac{	heta }{2}}{	an \dfrac{	heta }{2}}$$ if value of $$\cos 	heta =\dfrac{-5}{13}$$ in second quadrant.

Accepted Answer

$$\dfrac{2\sqrt{13}}{13}$$

Answer

$$\dfrac{2\sqrt{15}}{15}$$

Answer

$$\sqrt{15}$$

Answer

$$\sqrt{13}$$

Question 5

Calculate the value of $$\cos 8	heta $$

Accepted Answer

$$8{{\left( 2{{\cos }^{2}}	heta -1 ight)}^{4}}-16{{\cos }^{2}}	heta +9$$

Answer

$$4{{\left( 2{{\cos }^{2}}	heta -1 ight)}^{4}}-12{{\cos }^{2}}	heta +1$$

Answer

$$4{{\left( 2{{\cos }^{2}}	heta -1 ight)}^{4}}+12{{\cos }^{2}}	heta -1$$

Answer

$$8{{\left( 2{{\cos }^{2}}	heta +1 ight)}^{4}}+16{{\cos }^{2}}	heta -9$$