Question

If $\tan \left({89}^{\circ }{16}^{\prime }\right)$ = x then $\tan \left({269}^{\circ }{16}^{\prime }\right)$ = ___

• A. x/2
• B. x/3
• C. x
• D. 2x

Answer 1

The correct option is C x

We know that $\tan \left(A\right)=\tan (n\pi +A)$ for all values of $n$ and $\pi ={180}^o$
As ${269}^{o}16{}^{\prime }={180}^o+{89}^{o}16{}^{\prime }$
we have $\tan \left({269}^{o}16{}^{\prime }\right)=tan\left({89}^{o}16{}^{\prime }\right)=x$