If 4 tan-3- evaluate 4sin-cos-1-4 sin-cos-1-

nbsp;4 tan⁡θ=3 tan⁡θ =3/4 By applying pythagoras theorem, we will get sinθ = nbsp;3/5 cosθ = nbsp;4/5 4sinθ cosθ+1/ nbsp;4sin⁡θ+cos⁡θ 1 4(3/5) (4/5) ...

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Standard X

Mathematics

Standard Values of Trigonometric Ratios

If 4 tan⁡θ=3,...

Question

If 4 $tan θ = 3$ , evaluate $\frac{(4 sin θ - cos θ + 1)}{(4 sin θ + cos θ - 1)}$ .

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Solution

4 tan⁡θ=3
$tan θ = \frac{3}{4}$
By applying pythagoras theorem, we will get
$sin θ$ = $\frac{3}{5}$
$cos θ$ = $\frac{4}{5}$
$\frac{4 sin θ - cos θ + 1}{4 sin θ + cos θ - 1}$
$\frac{4 (\frac{3}{5}) - (\frac{4}{5}) + 1}{4 (\frac{3}{5}) + (\frac{4}{5}) - 1}$
$\frac{(\frac{12}{5}) - (\frac{4}{5}) + 1}{(\frac{12}{5}) + (\frac{4}{5}) - 1}$
= $\frac{13}{11}$

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If 4 tanθ=3, evaluate (4sinθ−cosθ+1)(4sinθ+cosθ−1).

4 tan⁡θ=3 tanθ=34 By applying pythagoras theorem, we will get sinθ = 35 cosθ = 45 4sinθ−cosθ+14sinθ+cosθ−1 4(35)−(45)+14(35)+(45)−1 (125)−(45)+1(125)+(45)−1 = 1311

If 4 $tan θ = 3$ , evaluate $\frac{(4 sin θ - cos θ + 1)}{(4 sin θ + cos θ - 1)}$ .