Half-angle identity Quiz 1

Question 1

For a $$\Delta ABC,$$ with sides $$a,b	ext{ and }c$$, its semi perimeter is the quantity$$s=\dfrac{a+b+c}{2}$$, find the value of $$1-	an \dfrac{A}{2}	an \dfrac{B}{2}$$.

Accepted Answer

$$\dfrac{2c}{a+b+c}$$

Answer

$$\dfrac{a+b+c}{2c}$$

Answer

$$\dfrac{\sqrt{2}c}{a+b+c}$$

Answer

$$\dfrac{c}{a+b+c}$$

Question 2

Let $$x$$is the length of fencing required for a triangular field $$\Delta ABC,$$then find the value of$$b{{\cos }^{2}}\dfrac{C}{2}+c{{\cos }^{2}}\dfrac{B}{2}$$.

Accepted Answer

$$\dfrac{x}{2}$$

Answer

$$\dfrac{3x}{2}$$

Answer

$$\dfrac{2x}{2}$$

Answer

$$x$$

Question 3

If $$2	an \left( \dfrac{x}{2} ight)=\left\{ 1-{{	an }^{2}}\left( \dfrac{x}{2} ight) ight\}\left( \sin 45{}^\circ \cos 45{}^\circ +\sin 30{}^\circ  ight)$$ then the value of $$x$$ is

Accepted Answer

$$x=45{}^\circ $$

Answer

$$x=55{}^\circ $$

Answer

$$x=40{}^\circ $$

Answer

$$x=90{}^\circ $$

Question 4

Find the value of $$\dfrac{\sqrt{3}}{2\sin 10{}^\circ \cos 10{}^\circ }-\dfrac{1}{\cos 20{}^\circ }$$.

Accepted Answer

4

Answer

8

Answer

2

Answer

1

Question 5

If $$x={{\sin }^{2}}	heta 	ext{ and }y={{\cos }^{2}}	heta $$ , find the value of $$\dfrac{{{x}^{4}}-{{y}^{4}}}{\sqrt{(y-x)}(1+y-x)}$$.

Accepted Answer

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

Answer

$$-\dfrac{1}{4}$$

Answer

$$-1$$

Answer

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