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  • Trigonometry
  • Trigonometric identities test
  • Sum and Difference Formulas

Sum and Difference Formulas

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  • Question 1:
    1 pts
    		Which identity is this? $$\cos\alpha\cos\beta-\sin\alpha\sin\beta$$

    $sin(\alpha + \beta)$

    $sin(\alpha - \beta)$

    $cos(\alpha + \beta)$

    $cos(\alpha - \beta)$

  • Question 2:
    1 pts
    		Which identity is this? $$\sin\alpha\cos\beta-\cos\alpha\sin\beta$$
    The sine of angle alpha plus angle beta.
    The sine of angle alpha minus angle beta.
    The cosine of angle alpha plus angle beta.
    The tangent of angle alpha plus angle beta.
  • Question 3:
    1 pts
    		$\sin20^{\circ}\cdot\cos10^{\circ}+\cos20^{\circ}\cdot\sin10^{\circ}=sin(30^{\circ})=\dfrac{1}{2}$
  • Question 4:
    1 pts
    		$\cos \dfrac{7\pi}{10}\cdot \cos\dfrac{\pi}{5}+\sin \dfrac{7\pi}{10}\cdot \sin \dfrac{\pi}{5}=1$
  • Question 5:
    2 pts
    		Use the angle sum identity to find the exact value of $\cos 105^{\circ}.$

    $\dfrac{\sqrt{2}+\sqrt{6}}{4}$

    $\dfrac{-\sqrt{2}-\sqrt{6}}{4}$

    $\dfrac{\sqrt{2}-\sqrt{6}}{4}$

    none of these

  • Question 6:
    2 pts
    		If $\tan\alpha=-\dfrac{3}{4}$ and $\alpha \in \left(\dfrac{\pi}{2}, \pi\right)$ then find the value of $\sin \left(\dfrac{\pi}{4}+\alpha\right).$
    $-\dfrac{4}{5}$
    $\dfrac{3}{5}$
    $-\dfrac{\sqrt{2}}{10}$
    $-\dfrac{7\sqrt{2}}{10}$
  • Question 7:
    2 pts
    		If $\sin \alpha=\sin\beta=\dfrac{5}{13}$ and $\alpha \in \left(0, \dfrac{\pi}{2}\right); \beta \in \left(\dfrac{\pi}{2},\pi\right)$ then find the value of $\cos(\alpha+\beta).$
    $\cos(\alpha+\beta)=$
  • Question 8:
    2 pts
    		Use the angle difference identity to find $\cos(x-\pi).$

    $\cos x$

    $-\cos x$

    $\sin x$

    $-\sin x$

  • Question 9:
    3 pts
    		Simplify the expression.
    $(\sin x+\sin y)^{2}+(\cos x+ \cos y)^{2}=$
  • Question 10:
    3 pts
    		Simplify the expression.
    $\dfrac{\sin{\dfrac{\pi}{7}}\cos\dfrac{2\pi}{7}+\cos\dfrac{\pi}{7}\sin\dfrac{2\pi}{7}}{\cos\dfrac{\pi}{7}\cos\dfrac{\pi}{14}+\sin\dfrac{\pi}{7}\sin\dfrac{\pi}{14}}=$
  • Question 11:
    3 pts
    		Simplify the expression.
    $\cos \left(\dfrac{\pi}{3}-\alpha\right)=$
  • Question 12:
    3 pts
    		If $\tan \alpha=\dfrac{1}{7}$ and $\alpha+\beta=\dfrac{\pi}{4}$ find $\tan \beta.$
    $\tan \beta=$

Angle Measurement

Right triangle

Unit circle

Trigonometric identities