Trigonometric substitution Quiz 1

Question 1

Evaluate and write the value of $${{	an }^{-1}}\left( \dfrac{4x}{1-4{{x}^{2}}} ight)$$.

Accepted Answer

$$2{{	an }^{-1}}2x$$

Answer

$$4{{	an }^{-1}}2x$$

Answer

$$6{{	an }^{-1}}2x$$

Answer

$$8{{	an }^{-1}}2x$$

Question 2

Solve the expression $${{\cot }^{-1}}\sqrt{\dfrac{1+4x}{1-4x}}$$ and write its value in the simplest form.

Accepted Answer

$$\dfrac{{{\cos }^{-1}}(4x)}{2}$$

Answer

$${{\cos }^{-1}}\left( \dfrac{2x}{5} \right)$$

Answer

$$\dfrac{{{	an }^{-1}}(4x)}{2}$$

Answer

$${{	an }^{-1}}\left( \dfrac{5x}{2} ight)$$

Question 3

Reduce the expression $${{\cos }^{-1}}\left( \dfrac{1-{{t}^{2}}}{1+{{t}^{2}}} \right)$$ into simplest form at $$t=1$$

Accepted Answer

$$\dfrac{\pi }{2}$$

Answer

$$\dfrac{\pi }{4}$$

Answer

$$\dfrac{\pi }{6}$$

Answer

$$\dfrac{\pi }{12}$$

Question 4

What is the equivalent expression of the trigonometric expression $${{	an }^{-1}}\left( \dfrac{1-	an M}{1+	an M} ight)$$

Accepted Answer

$$\dfrac{\pi }{4}-M$$

Answer

$$\dfrac{\pi }{4}+M$$

Answer

$$\dfrac{\pi }{4}+2M$$

Answer

$$\dfrac{\pi }{4}-2M$$

Question 5

If $$Z={{\sin }^{-1}}16x\sqrt{1-64{{x}^{2}}},$$ then write the value of $$Z$$ in simplified form.

Accepted Answer

$$2{{\sin }^{-1}}(8x)$$

Answer

$$2{{\sec }^{-1}}(8x)$$

Answer

$$2{{	an }^{-1}}(8x)$$

Answer

$$2co{{t}^{-1}}(8x)$$