Question

if codec theta=13/12, then evaluate 2sintheta-3costheta/4sintheta-9costheta​

Answer 1

Answer:

Answer:

312/25

Step-by-step explanation:

Given that

tan \begin{gathered}\theta\\\end{gathered}

θ

= 12/13

To Evaluate

\frac{2 Sin\theta \ Cos\theta}{Cos^2\theta - Sin^2\theta}

Cos

2

θ−Sin

2

θ

2Sinθ Cosθ

Divide Numerator and Denominator by Cos^2\thetaCos

2

θ

\frac{\frac{2 Sin\theta \ Cos\theta}{Cos^2\theta} }{\frac{Cos^2\theta - Sin^2\theta}{Cos^2\theta} }

Cos

2

θ

Cos

2

θ−Sin

2

θ

Cos

2

θ

2Sinθ Cosθ

=> \frac{2 tan\theta}{1 - tan^2\theta}

1−tan

2

θ

2tanθ

=> \begin{gathered}\frac{2 *\frac{12}{13}}{1 - (\frac{12}{13})^2 } \\ \\= > \frac{ \frac{24}{13} }{1 - \frac{144}{169} }\\\\=> \frac{\frac{24}{13} }{\frac{25}{169} } \\\\=> \frac{24}{13} * \frac{169}{25} \\\\=> \frac{312}{25}\end{gathered}

1−(

13

12

)

2

2∗

13

12

=>

1−

169

144

13

24

=>

169

25

13

24

=>

13

24

∗

25

169

=>

25

312