Quotient identities Quiz 1

Question 1

Find the quotient if $$(1-sin^2	heta)(cos^2	heta)$$ is divided by $$2cos^4	heta$$.

Accepted Answer

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

Answer

0

Answer

1

Answer

2

Question 2

Find the value of an acute-angle $$\delta $$ if it is given that $$7si{{n}^{2}}\delta +3co{{s}^{2}}\delta =4$$

Accepted Answer

$$30{}^\circ $$

Answer

$$45{}^\circ $$

Answer

$$60{}^\circ $$

Answer

$$25{}^\circ $$

Question 3

What is the value of $$\sqrt{3}tan\alpha +1$$ if $$\left( 4{{r}^{3}}+57r-21 \right)sin\alpha =1$$ and $$\left( 4{{r}^{3}}+57r-21 \right)cos\alpha =\sqrt{3}$$?

Accepted Answer

2

Answer

1

Answer

0

Answer

-1

Question 4

Find the value of $$3{{\csc }^{2}}	heta +5\cos 	heta $$ if $$	heta $$ is an acute-angle and $$\dfrac{co{{s}^{2}}	heta }{\left( co{{t}^{2}}	heta - co{{s}^{2}}	heta  ight)}=3$$.

Accepted Answer

$$6.5$$

Answer

$$4.5$$

Answer

$$3.33$$

Answer

$$7.5$$

Question 5

If $$\cos X=m\cos Y$$and where $$X
e Y$$and their values range from $$0	ext{ to }\dfrac{\pi }{2}$$, then which of the following is true?

Accepted Answer

$$\cot \left( \dfrac{X+Y}{2} ight)=\dfrac{m+1}{m-1}	imes 	an \left( \dfrac{Y-X}{2} ight)$$

Answer

$$\cot \left( \dfrac{X+Y}{2} ight)=\dfrac{{{m}^{2}}+m+1}{{{m}^{2}}+m-1}	imes 	an \left( \dfrac{Y-X}{2} ight)$$

Answer

$$\cot \left( \dfrac{X+Y}{2} ight)=\dfrac{2m+1}{2m-1}	imes 	an \left( \dfrac{X-Y}{2} ight)$$

Answer

$$\cot \left( \dfrac{X+Y}{2} ight)=\dfrac{m+1}{m-1}	imes \cot \left( \dfrac{Y-X}{2} ight)$$