Question

if tan22°+tan38°-√3=ktan22°tan38° then k=

Answer 1

Answer:

the value of the k in above equation is -√3

Answer 2

Answer:

The value of $k = \sqrt{3}$

Step-by-step explanation:

As per the question,

We have to find the value of k in the equation $tan22\°+tan38\° - \sqrt{3} = k(tan22\°\times tan38\°)$

As we know that,from the trigonometric identity,

$tan(A+B) = \frac{tanA+tanB}{1-tanA\times tanB}$

So,

$tan (22\°+38\°) =  tan60\°$

$tan60\° =\frac{tan22\°+tan38\°}{1-tan22\°\times tan38\°}$

$\sqrt{3} = \frac{tan22\°+tan38\°}{1-tan22\°\times tan38\°}$

$\sqrt{3} \times (1-tan22\°\times tan38\°) = tan22\°+tan38\°$

$\sqrt{3} - \sqrt{3} (tan22\°\times tan38\°) = tan22\°+tan38\°$

$tan22\°+tan38\° - \sqrt{3} = \sqrt{3} (tan22\°\times tan38\°)$

Hence,the value of $k = \sqrt{3}$.