Question

if tanA=1/root3 find the value of sinA×cosB+cosA×sinB

Answer 1

Given : tan A=1/root3
draw a right angle triangle ABC right angled at C
put the value of tan in the triangle
we get:
${ab}^{2} = {ac}^{2} + {bc}^{2} \\ {ab}^{2} = (\sqrt{3 }) ^{2} + 1 \\ {ab}^{2} = 3 + 1 \\ {ab}^{2} = 4 \\ ab = \sqrt{4 } \\ ab = 2$
$\sin(a) = \frac{1}{2} \\ \cos(b) = \frac{ \sqrt{3} }{2} \\ \sin(b) = \frac{ \sqrt{3} }{2} \\ \cos(b) = \frac{1}{2}$
put this value in the question
$\sin(a ) \times \cos(b) + \cos(a) \times \sin(b)$
we get
$\frac{1}{2} \times \frac{1}{2} + \frac{ \sqrt{3} }{2 } \times \frac{ \sqrt{3} }{2} \\ \frac{1}{4} + \frac{3}{4} \\ \frac{4}{4} = 1$