Trigonometric Identities Quiz 1

Question 1

Write the value of $${{3}^{{{\left[ co{{\sec }^{2}}\frac{m}{2}-{{\cot }^{2}}\frac{m}{2} \right]}^{3}}}}$$.

Accepted Answer

$$3$$

Answer

$$1$$

Answer

$$0$$

Answer

$$4$$

Question 2

Simplify $$\log \left( \dfrac{{{\sec }^{2}}\dfrac{7\ell }{5}-{{	an }^{2}}\dfrac{7\ell }{5}}{{{\cot }^{2}}\dfrac{9\ell }{17}-\cos e{{c}^{2}}\dfrac{9\ell }{17}} ight)$$.

Accepted Answer

not defined

Answer

$$0$$

Answer

$$1$$

Answer

$$2$$

Question 3

Which of the following could be the value of $$\cos \,23g$$

Accepted Answer

$$2\,{{\cos }^{2}}\,\,\dfrac{23g}{2}-1$$

Answer

$$1-2{{\cos }^{2}}\left( \dfrac{23g}{2} \right)$$

Answer

$$2{{\sin }^{2}}\left( \dfrac{23g}{2} \right)-1$$

Answer

$${{\cos }^{2}}\,\,\dfrac{23g}{2}+1$$

Question 4

Write the simplified form of $$\dfrac{\sin \,\left( \dfrac{37x}{2} \right)\,\,\,-\,\,\sin \,\,\left( \dfrac{29x}{2} \right)}{\sin \,\,33x}$$.

Accepted Answer

$$\dfrac{\sin \,2x}{\sin \,\left( \dfrac{33x}{2} \right)}$$

Answer

$$\dfrac{\cos \,\,x}{\cos \,\left( \dfrac{33x}{2} \right)}$$

Answer

$$\dfrac{\sin \,x}{\cos \,\left( \dfrac{33x}{2} \right)}$$

Answer

$$\dfrac{\cos \,x}{\sin \,\left( \dfrac{33x}{2} \right)}$$

Question 5

If $$y\,=\,\sqrt{1+\cos \left( \dfrac{3x}{17} \right)}$$, then write the value of $$2y\sin \left( \dfrac{3x}{34} \right)$$.

Accepted Answer

$$\sqrt{2}\,\sin \left( \dfrac{3x}{17} \right)$$

Answer

$$\sqrt{2}\,\cos \left( \dfrac{3x}{17} \right)$$

Answer

$$\sqrt{2}\,	an \left( \dfrac{3x}{17} ight)$$

Answer

$$\sqrt{2}\,\cot \left( \dfrac{3x}{17} \right)$$