Question

solve the above question​

Answer 1

The value of trigonometry expression is $\Rightarrow \dfrac{93}{149}$

Step-by-step explanation:

Given: $4\cos\theta=11\sin\theta$

To evaluate: $\dfrac{11\cos\theta-7\sin\theta}{11\cos\theta+7\sin\theta}$

Using trigonometry identity

$4\cos\theta=11\sin\theta$

$\tan\theta=\dfrac{4}{11}$    

$\Rightarrow \dfrac{11\cos\theta-7\sin\theta}{11\cos\theta+7\sin\theta}$

Divide by cos at numerator and denominator

$\Rightarrow \dfrac{\dfrac{11\cos\theta-7\sin\theta}{\cos\theta}}{\dfrac{11\cos\theta+7\sin\theta}{\cos\theta}}$

$\Rightarrow \dfrac{11-7\tan\theta}{11+7\tan\theta}$

Substitute the value of tan

$\Rightarrow \dfrac{11-7\times \dfrac{4}{11}}{11+7\times \dfrac{4}{11}}$

$\Rightarrow \dfrac{121-28}{121+28}$

$\Rightarrow \dfrac{93}{149}$

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