Question

find the value of( 11/cot^2 theta - 11/ cos^2) theta​

Answer 1

$\frac{11}{cot^2\theta}-\frac{11}{cos^2\theta}$

$=11(\frac{1}{cot^2\theta})-11(\frac{1}{cos^2\theta})$

$=11tan^2\theta-11sec^2\theta$

$=11(tan^2\theta-sec^2\theta)$

$=-11(sec^2\theta-tan^2\theta)$

$\text{using}$

$\boxed{\bf\,sec^2\theta-tan^2\theta=1}$

$\text{we get}$

$=11(1)$

$=-11$

$\implies\boxed{\bf\,11(\frac{11}{cot^2\theta})-(\frac{11}{cos^2\theta})=-11}$

Answer 2

The value of $(\dfrac{11}{\cot^2\theta}-\dfrac{11}{\cos^2\theta})$ is (-11).

Step-by-step explanation:

We need to find the value of $(\dfrac{11}{\cot^2\theta}-\dfrac{11}{\cos^2\theta})$

So,

$=(\dfrac{11}{\cot^2\theta}-\dfrac{11}{\cos^2\theta}) \\ \\=11(\dfrac{1}{\cot^2\theta}-\dfrac{1}{\cos^2\theta}})$

Since,

$\dfrac{1}{\cot^2\theta}=\tan^2\theta\\\\\dfrac{1}{\cos^2\theta}=\sec^2\theta$

So,

$=11(\tan^2\theta-\sec^2\theta)$

Since we know that, $\sec^2\theta-\tan^2\theta=1$

So,

$(\dfrac{11}{\cot^2\theta}-\dfrac{11}{\cos^2\theta})=11(\tan^2\theta-\sec^2\theta)\\\\(\dfrac{11}{\cot^2\theta}-\dfrac{11}{\cos^2\theta})=11(-1)\\\\(\dfrac{11}{\cot^2\theta}-\dfrac{11}{\cos^2\theta})=-11$

So, the value of $(\dfrac{11}{\cot^2\theta}-\dfrac{11}{\cos^2\theta})$ is (-11).

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Trigonometry