Inverse trigonometric ratios Quiz 1

Question 1

Find $$\int{\dfrac{{{x}^{4}}}{{{x}^{10}}+{{\alpha }^{2}}{{\beta }^{2}}}dx}$$.

Accepted Answer

$$\dfrac{1}{5\alpha \beta }{{	an }^{-1}}\left( \dfrac{{{x}^{5}}}{\alpha \beta } ight)+c$$

Answer

$${{	an }^{-1}}\left( \dfrac{{{x}^{5}}}{\alpha \beta } ight)+c$$

Answer

$$\dfrac{1}{5\alpha \beta }{{\cot }^{-1}}\left( \dfrac{{{x}^{5}}}{\alpha \beta } \right)+c$$

Answer

$$\dfrac{1}{3}{{	an }^{-1}}\left( {{x}^{5}} ight)+c$$

Question 2

Evaluate: $$\cos \left( a+b \right)$$ where $$a={{\csc }^{-1}}\left( 4 \right)$$ and $$b={{\sec }^{-1}}\dfrac{4}{3}$$.

Accepted Answer

$$\dfrac{3\sqrt{15}-\sqrt{7}}{16}$$

Answer

$$\dfrac{15\sqrt{5}+\sqrt{7}}{16}$$

Answer

$$\dfrac{6\sqrt{15}-3\sqrt{7}}{4}$$

Answer

$$\dfrac{5\sqrt{3}-2\sqrt{7}}{8}$$

Question 3

Find the combined value of $$\sin \left( 2{{	an }^{-1}}\dfrac{2}{3} ight)$$ and $$\cos \left( {{	an }^{-1}}\sqrt{3} ight)$$.

Accepted Answer

$$\dfrac{37}{26}$$

Answer

$$\dfrac{121}{144}$$

Answer

$$\dfrac{-120}{169}$$

Answer

$$\dfrac{35}{26}$$

Question 4

Find the value of $$'x'$$ if it is given that $$	an \left( a+b ight)=1$$, where $$	an a=\dfrac{x-1}{x-2}$$ and $$	an b=\dfrac{x+1}{x+2}$$.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 5

Find the difference between the angles of $$2{{\sin }^{-1}}\dfrac{3}{5}$$ and $${{	an }^{-1}}\dfrac{17}{31}$$.

Accepted Answer

$$45{}^\circ $$

Answer

$$90{}^\circ $$

Answer

$$30{}^\circ $$

Answer

$$60{}^\circ $$