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Question
In a ΔABC, right angled at A, if tan C = `sqrt3` , find the value of sin B cos C + cos B sin C.
Solution
In a Δle ABC right angled at A tan C = `sqrt3`
Find sin B cos C + cos B sin C
`tan c = sqrt3`
`tan c = "oppoite side"/"adjacent side"`
Let x be the hypotenuse By applying Pythagoras we get
`BC^2 = BA^2 + AC^2`
`x^2 = (sqrt3)^2 + 1^2`
x2 = Δ ⇒ x = 2
At ∠B, `sin B = (AC)/(BC) = 1/2`
`cos B = sqrt3/2`
At ∠C, `sin = sqrt3/2`
`cos c = 1/2`
On substitution we get
`=> 1/2 xx 1/2 + sqrt3/2 xx sqrt3/2`
`=> 1/4 + (sqrt3)/4 xx (sqrt3) = (sqrt3 xx sqrt3 + 1)/4 = (3 + 1)/4 = 4/4 = 1`
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