In A ABC, right angled at A, of at A, of Tan C=13 . find the value of sinB cosC + cosB sinC
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In A ABC, right angled at A, of at A, of Tan C=13 . find the value of sinB cosC + cosB sinC
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Answer:
In right angled Δ ABC,
Given, tanC=3
We know that, tanθ=adjacent side to∠θopposite side to∠θ
∴AB=3 and AC=1
From Pythagoras theorem,
BC2=AB2+AC2
BC2=(3)2+12
BC2=3+1=4
BC=2
sinθ=hypotenuseopposite side to∠θ
cosθ=hypotenuseadjacent side to∠θ
sinB=BCAC=21
cosB=BCAB=23