Question

If 4 tan = 3, find 4 sin +cos/ 4−cos

Answer 1

4tan = 3 ⇒ tan = 3/4

we know, tan = perpendicular/base

so, after comparing , perpendicular = 3 and base = 4

∴ hypotenuse = √(3² + 4²) = 5

now, sin = perpendicular/hypotenuse = 3/5

cos = base/hypotenuse = 4/5

now, (4sin - cos + 1)/(4sin + cos - 1)

= (4 × 3/5 - 4/5 + 1)/(4 × 3/5 + 4/5 - 1)

= (12 - 4 + 5)/(12 + 4 - 5)

= 13

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