√3(tan11+tan19) +tan11tan19
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Answered by
7
Step-by-step explanation:
Given √3 (tan 11 + tan 19) + tan 11 tan 19
Given we need to find the value of √3 (tan 11 + tan 19) + tan 11 tan 19---------1
We know that tan (A + B) = tan A + tan B / 1 – tan A tan B
So tan (11 + 19) = tan 11 + tan 19 / 1 – tan 11 tan 19
We know that tan (11 + 19) = tan 30 = 1 / √3
So 1/√3 = tan 11 + tan 19 / 1 – tan 11 tan 19
So √3 (tan 11 + tan 19) = 1 – tan 11 tan 19
Substituting this in 1 we get
1 – tan 11 tan 19 + tan 11 tan 19
= 1
Answered by
0
11+19=30
=>tan(11+19)°=tan30°
=>(tan11°+tan19°)/(1-tan11°tan19°)=1/√3
cross multiplication
=>√3(tan11°+tan19°)=1-tan11°tan19°
=>√3(tan11°+tan19°)+tan11°tan19°=1
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