Question

please prove it............​

Answer 1

Answer:

cot( 105 ) - tan( 105 ) = $2\sqrt{3}$

Step-by-step explanation:

Tan15 = tan(45–30)

=( tan 45 - tan 30)(1+tan45tan30)  

=(1 - 1/√3)/(1+1 × 1/√3)  

=(√3–1)/(√3+1). So  

   cot 105 - tan 105

= cot(90+15) - tan(90+15)  

= - tan 15 + cot15

= - [{(√3–1)/(√3+1)}-(√3+1)/(√3–1)]  

= - [{(√3–1)^2 - (√3+1)^2}/(3–1)

=-(-4√3)/2

= 2√3.

Hope it helps u and mark it as brainliest plz

Answer 2

Answer:

hello ☺☺

Tan15 = tan(45–30)

=( tan 45 - tan 30)(1+tan45tan30)

=(1 - 1/√3)/(1+1 × 1/√3)

=(√3–1)/(√3+1). So

cot 105 - tan105= cot(90+15) - tan(90+15)

=- tan 15 + cot15 =-[{(√3–1)/(√3+1)}-(√3+1)/(√3–1)]

= - [{(√3–1)^2 - (√3+1)^2}/(3–1)

=-(-4√3)/2 = 2√3.