Question

if 5 sin tita =4evaluate 5sin tita-3cos tita /5sin tita +2cos tita
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Answer 1

Answer:

11/26

Step-by-step explanation:

take a right angled triangle ABC right angled at B. So that makes BC the hypotenuse. i suggest you drawing it in your notebook. mark angle CAB as theta ( or tita , whatever you call it. ). then take BC as 4x units and AC as 5x units [ since sin theta = opposite divided by hypotenuse . opposite is BC. hypotenuse is AC. we need not find the value of x. the ratio itself is 4x/5x = 4/5 ( given in the question ). now use pythagoras theorem to get the value of side AB. AB = sqrt(AC^2-BC^2) = sqrt(25x^2 - 16x^2) = sqrt(9x^2) = 3x.

now we have all sides of triangle.

sin theta = 4/5

cos theta = adjacent/hypotenuse = AB/AC = 3x/5x = 3/5

there !! you have it.

put it in the question given to you and solve it.

numerator : 5 sin theta - 3 cos theta = 4 - 9/5 = 11/5

denominator : 5 sin theta + 2 cos theta = 4 + 6/5 = 26/5

so final answer is 11/26