Cofunction identities Quiz 1

Question 1

Evaluate: $$\sin 33{}^\circ \sin 39{}^\circ \sec 57{}^\circ \sec 51{}^\circ $$

Accepted Answer

$$1$$

Answer

$$-1$$

Answer

$$0$$

Answer

$$3$$

Question 2

If the combined value of $$A	ext{ and }B$$ is $$\dfrac{\pi }{2}$$, find the value of $$\left( 1-{{\sin }^{2}}A ight)\left( 1-{{\cos }^{2}}A ight)	imes \left( 1+	ext{co}{{	ext{t}}^{2}}B ight)(1+	ext{ta}{{	ext{n}}^{2}}B)$$.

Accepted Answer

$$1$$

Answer

$$-1$$

Answer

$$0$$

Answer

$$3$$

Question 3

Find the value of $$\cos A	imes \dfrac{1}{\sin B}-\cos A	imes \dfrac{1}{	ext{ cosec }B}$$ such that $$A$$ and $$B$$ are two complementary angles.

Accepted Answer

$$\sin^{2}A$$

Answer

$$sinA$$

Answer

$$sin2A$$

Answer

$$2\sin^{2}A$$

Question 4

Find the value of $$\left\{ {{\sec }^{-1}}(x-y) \right\}$$ where y ranges from $$\left( 0,\dfrac{\pi }{4} \right)$$ and $$\sin (x+y)=1$$.

Accepted Answer

$$sin2y$$

Answer

$$\sin y$$

Answer

$$\sin^{2}y$$

Answer

$$2\sin^{2}y$$

Question 5

Find the value of $$\sqrt{	ext{cosec }A\cos ecB	imes \dfrac{1}{\left\{ \left( \dfrac{\sin A}{\sin B} ight)+\left( \dfrac{\cos A	ext{ }}{\cos B	ext{ }} ight) ight\}}}$$ such that $$A	ext{ and }B$$ are two complementary angles.

Accepted Answer

$$1$$

Answer

$$-1$$

Answer

$$0$$

Answer

$$3$$