Trigonometry -- Addition Formulae

 $\tan\left(60\degree+45\degree\right)=\tan60\degree+\tan45\degree$  . True or False?

• True

• False

• Cannot be determined

Tags

CCSS.HSF.TF.C.9

Which of the following is/are feasible to find the exact value of

 $\tan\ \left(\frac{\pi}{12}\right)$  ? (You may select more than one answer.)

•  $\tan\ \left(\frac{\pi}{12}\right)=\tan\left(\frac{\pi}{4}-\frac{\pi}{6}\right)$  

•  $\tan\ \left(\frac{\pi}{12}\right)=\tan\left(\frac{\pi}{3}-\frac{\pi}{4}\right)$  

•  $\tan\ \left(\frac{\pi}{12}\right)=\tan\left(\frac{\pi}{24}+\frac{\pi}{24}\right)$  

•  $\tan\left(\frac{\pi}{12}\right)=\tan\left(\frac{\pi}{5}-\frac{7\pi}{60}\right)$  

• All of the above

Without using a calculator, find the exact value of

 $\sin50\degree\cos20\degree-\cos50\degree\sin20\degree.$  

Tags

CCSS.HSF.TF.C.9

Write the following expression as a function of a single angle:

 $\cos x\cos2x+\sin x\sin2x.$  

Which of the following is the correct approach to solve the equation:

 $\tan5x=\tan2x$  ?

• Subtract  $2x$   from both sides. So,  $\tan3x=\tan0$  . Then solve.

•   $\tan\left(\frac{5}{2}x\right)=1$  . Then solve.

• Express  $\tan5x\ =\ \tan\left(3x+2x\right).$  Then expand using addition formula. Cross multiply and solve.

• None of the above.

Solve

 $\tan5x=\tan2x$  for  $0^{ }<x<\pi$  .  (You may select more than one answer.)

•  $\frac{\pi}{6}$  

•  $\frac{\pi}{5}$  

•  $\frac{\pi}{4}$  

•  $\frac{\pi}{3}$  

•  $\frac{2\pi}{3}$