in triangle ABC angle C=90°.if tanA=1÷root3.find the value of sinA cosB+cosA×sinB​

Question

in triangle ABC angle C=90°.if tanA=1÷root3.find the value of sinA cosB+cosA×sinB​

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Sadie 3 weeks 2021-10-01T16:17:52+00:00 1 Answer 0 views 0

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    2021-10-01T16:19:36+00:00

    In triangle ABC Angle C = 90.

    Since

     \tan(a)  =  \frac{1}{ \sqrt{3} }

    But tan30=1/√3

    => A=30°

    Since In a triangle sum of all angles is 180°.

    Therefore,

    A+B+C=180°

    =>30°+B+90°=180°

    B=60°

    Now

    SinACosB+CosASinB=Sin30 Cos60 + Cos30 Sin60

     \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

    Hope it is helpful

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