Question

prove that. tan69° + tan 66°+1= tan69°tan66°

Answer 1

hope u understand mark it as brainliest..

Answer 2

Answer:

$\tan 69 ^ { \circ } \tan 66 ^ { \circ } = 1 + \tan 66 ^ { \circ } + \tan 69 ^ { \circ }$

Hence proved

Solution:

We know that

$\begin{aligned} \tan ( A + B ) & = \frac { \tan A + \tan B } { 1 - \tan A \tan B } \\\\ \tan \left( 69 ^ { \circ } + 66 ^ { \circ } \right) & = \frac { \tan 69 ^ { \circ } + \tan 66 ^ { \circ } } { 1 - \tan 69 ^ { \circ } \tan 66 ^ { \circ } } \\\\ \tan 135 ^ { \circ } & = \frac { \tan 69 ^ { \circ } + \tan 66 ^ { \circ } } { 1 - \tan 69 ^ { \circ } \tan 66 ^ { \circ } } \end{aligned}$

We know $\tan 135^{\circ} =-1$ since $\tan \frac{3\pi}{4} =-1$

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

$\tan 69 ^ { \circ } + \tan 66 ^ { \circ } = - 1 + \tan 69 ^ { \circ } \tan 66 ^ { \circ }$

$\tan 69 ^ { \circ } \tan 66 ^ { \circ } = 1 + \tan 66 ^ { \circ } + \tan 69 ^ { \circ }$

Hence proved