Question

solve plsss



full expain



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Answer 1

5.66

Step-by-step explanation:

On solving the 1st equation we get tan theta =3/4

so theta = 37 (basic trigonometry )

so substitution we get tan (5.6)=0.09

Happy??

Answer 2

Question :-

If 3 cosθ = 4 sinθ, then what is the value of tan(45° + θ) ?

$\large\underline{\sf{Solution-}}$

Given that,

$\rm \: 3cos\theta = 4sin\theta$

can be further rewritten as

$\rm \: \dfrac{sin\theta }{cos\theta } = \dfrac{3}{4}$

$\rm\implies \:tan\theta = \dfrac{3}{4} - - - (1)$

Now, Consider

$\rm \: tan(45 \degree \: + \: \theta)$

We know,

$\boxed{ \rm{ \:tan(x + y) = \dfrac{tanx + tany}{1 - tanx \: tany} \: }}$

So, using this identity, we get

$\rm \: = \: \dfrac{tan45\degree + tan\theta }{1 - tan45\degree \: tan\theta }$

$\rm \: = \: \dfrac{1 + tan\theta }{1 - tan\theta }$

So, on substituting the value from equation (1), we get

$\rm \: = \: \dfrac{1 + \dfrac{3}{4} }{1 - \dfrac{3}{4} }$

$\rm \: = \: \dfrac{\dfrac{4 + 3}{4} }{\dfrac{4 - 3}{4} }$

$\rm \: = \: \dfrac{\dfrac{7}{4} }{\dfrac{1}{4} }$

$\rm \: = \: 7$

Hence,

$\rm\implies \:\rm \: tan(45 \degree \: + \: \theta) = 7$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{sin(x - y) = sinx \: cosy \: - \: siny \: cosx}\\ \\ \bigstar \: \bf{sin(x + y) = sinx \: cosy \: + \: siny \: cosx}\\ \\ \bigstar \: \bf{cos(x + y) = cosx \: cosy \: - \: sinx \: siny}\\ \\ \bigstar \: \bf{cos(x - y) = cosx \: cosy \:+\: siny \: sinx}\\ \\ \bigstar \: \bf{tan(x + y) = \dfrac{tanx + tany}{1 - tanx \: tany} }\\ \\ \bigstar \: \bf{tan(x - y) = \dfrac{tanx - tany}{1 + tanx \: tany} }\\ \\ \end{array} }}\end{gathered}\end{gathered}\end{gathered}$