Question

If tan (A-B)=1/root3 & sin A=1/root2, find the value of B​

Answer 1

Step-by-step explanation:

As tanA =1 , so, one of the value of A is π/4 , similarly as tanB= √3, one of the value of B= π/3

Therefore,

Cos (A+B) = cos(π/4 + π/3)

= Cosπ/4 *Cosπ/3 – Sinπ/4* Sinπ/3 , putting sin and cos value of π/4 & π/3

= (1/√2) *(1/2) - (1/√2) *(√3/2)

=(1/2√2) – (√3/2√2)

= (1-√3)/2√2 , multiplying both numerator and denominator by √2 , we get

= √2(1–√3)/4

Answer 2

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