If 4tan- -3- evaluate 4sin- -cos- -14sin- -cos- -1

4 tanθ =3 nbsp;⇒tanθ =34sinθ =3√(3^2+4^2)=35cosθ =4√(3^2+4^2)=45 nbsp;(4 sinθ cosθ +14 sin nbsp; θ +cosθ 1)=4 (35) (45)+14 (35)+ (45) 1=12 4+512+4 5=13 ...

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Byju's Answer

Standard XII

Mathematics

Principal Solution of Trigonometric Equation

If 4tanθ =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

$4 tan θ = 3$
$\Rightarrow tan θ = \frac{3}{4}$

$sin θ = \frac{3}{\sqrt{3^{2} + 4^{2}}} = \frac{3}{5}$
$cos θ = \frac{4}{\sqrt{3^{2} + 4^{2}}} = \frac{4}{5}$
$(\frac{4 sin θ - cos θ + 1}{4 sin θ + cos θ - 1}) = \frac{4 (\frac{3}{5}) - (\frac{4}{5}) + 1}{4 (\frac{3}{5}) + (\frac{4}{5}) - 1}$

$= \frac{12 - 4 + 5}{12 + 4 - 5} = \frac{13}{11}$

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If 4tanθ=3, evaluate (4sinθ−cosθ+14sinθ+cosθ−1)

4tanθ=3 ⇒tanθ=34sinθ=3√32+42=35cosθ=4√32+42=45(4sinθ−cosθ+14sinθ+cosθ−1)=4(35)−(45)+14(35)+(45)−1=12−4+512+4−5=1311

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