Question

show that tan(15°) = 2 - √(3)

Answer 1

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

Let A =45
B=30
we know that
tan 45=1
tan 30= 1/√3

LHS = tan 15
RHS = (tan 45 -tan 30)/(1+tan45 *tan 30)
= (1- 1/√3)/ (1 +1√3)
= (√3-1)/(√3+1)
= (√3-1)^2/ (√3+1)* (√3-1)
= (3+1-2√3)/(3-1)
=(4-2√3)/2
= 2-√3
Hence proved

Answer 2

Step-by-step explanation:

Given above

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