Question

pls solve this question! No spammers please . Please don't be greedy for 50 points . earn it with a correct explanation . Best explanation will be marked brainliest . I NEED A STEP BY STEP EXPLANATION PLEASE. ​ class 11​ .P.S : THE ANSWER IS PART D ) I, NEED THE EXPLANATION ​

Answer 1

Answer:

The Answer will be 1/√3.

Explanation:

= tan 75° - tan15° - √3 tan 75° tan 25°

tan 60° = √3

= tan (75-15) = √3

= tab 75° - tan15°/1 + tan75° tan15° = √3

= tan 75° - tan15° = √3 + √3 tan 75° tan15°

= tan 75° - tan15° - √3 tan 75° tan15° = √3

Hope it will be helpful :)...✍️

Answer 2

ANSWER ::

TO FIND ::

tan(5π/12) - tan(π/12) - √3 tan(5π/12) tan(π/12)

SOLUTION ::

We know that

tan 60° = √3

⟹ tan(75° - 15°) = √3 - - - - - - - - (1)

Now we proceed to apply the trigonometric formula

tan ( A - B) = ( tanA - tanB) / ( 1 + tanA tanB)

So from (1)

( tan75° - tan15°) / ( 1+ tan75° tan15°) = √3

On cross multiplication

( tan75° - tan15°) = √3 ( 1+ tan75° tan15°)

⟹ ( tan75° - tan15°) = √3 + √3 tan75° tan15°

⟹ tan75° - tan15° - √3 tan75° tan15° = √3

⟹ tan(5π/12) - tan(π/12) - √3 tan(5π/12) tan(π/12) = √3

HENCE THE REQUIRED VALUE = √3

SO THE CORRECT OPTION IS (d)