Question

In tan theta =4/3, find the value of 5 sin theta +2 cos theta /3 sin theta -cos theta​

Answer 1

Answer:

26/9

Step-by-step explanation:

      Given that: tanθ = 4/3

      To find: Value of 5sinθ +2 cosθ / 3sinθ -cosθ

      Solution:

          tanθ = 4/3 = opposite/adjacent

          Hypotenuse =

                                    $\sqrt{(4x)^{2} + (3x)^{2} } \\\\\sqrt{16x^{2} +9x^{2} } \\\\\sqrt{25x^{2} } \\\\= 5x$

          5sinθ +2cosθ / 3sinθ - cosθ

          (5 × 4/5 + 2×3/5) / (3×4/5 - 3/5)

          (4+6/5) / (12/5 - 3/5)

          (26/5) / (9/5)

          26/5 × 5/9

          26/9

          ∴ Therefor the value is:

             ${\boxed {\underline{\sf{\underline\orange{26/9 }}}}}$

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