Question

If $\tan {69}^{\circ }+\tan {66}^{\circ }-\tan {69}^{\circ }\tan {66}^{\circ }=2k,then2k=$

• A. $-1$
• B. $\frac{1}{2}$
• C. $-\frac{1}{2}$
• D. none

Answer 1

Answer: (A)

$-1$

We know

$\tan (69+66)=\frac{\tan 69+\tan 66}{1-\tan 69\tan 66}$

$=\tan 135=\frac{\tan 69+\tan 66}{1-\tan 69\tan 66}$

$=-1=\frac{\tan 69+\tan 66}{1-\tan 69\tan 66}$

$=\tan 69\tan 66-1=\tan 69+\tan 66$

$=\tan 69+\tan 66-\tan 69\tan 66=-1$

$=2k$

$=2k=-1$

Hence answer $2k=-1$