Question

the value of 9cottheta-9cosectheta​

Answer 1

$\small {\boxed {\bf Question:-}}$

Find the value of :-

$\bf 9cot^2\theta-9cosec^2\theta$

$\small \boxed {\bf Solution : - }$

$\leadsto \bf 9cot^2\theta -9cosec^2\theta$

$\leadsto \bf 9( {cosec}^{2} \theta - 1) - 9 {cosec }^{2} \theta$

$\leadsto \bf 9cosec^2\theta -9 - 9 {cosec}^{2} \theta$

$\leadsto \bf \cancel {9cosec^2\theta}-9 - \cancel{9cosec^2\theta}$

$\leadsto\underline {\boxed {\mathfrak {9cot^2\theta-9cosec^2\theta=-9}}}$

$\small \boxed {\bf Identities \: used : - }$

$\leadsto \bf cot^2\theta=cosec^2\theta-1$

$\small \boxed {\bf Know ~more:-}$

$\leadsto \bf cos^2\theta + {sin}^{2} \theta = 1$

$\leadsto \bf 1 + {tan}^{2} \theta = {sec}^{2} \theta$

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I hope that you are able to comprehend my working!

Answer 2

$\leadsto \bf 9cot^2\theta -9cosec^2\theta$

$\leadsto \bf 9( {cosec}^{2} \theta - 1) - 9 {cosec }^{2} \theta$

$\leadsto \bf 9cosec^2\theta -9 - 9 {cosec}^{2} \theta$

$\leadsto \bf \cancel {9cosec^2\theta}-9 - \cancel{9cosec^2\theta}⇝ </p><p>$

$\leadsto\underline {\boxed {\mathfrak {9cot^2\theta-9cosec^2\theta=-9}}}$

$\small \boxed {\bf Identities \: used : - } </p><p>$

$\leadsto \bf cot^2\theta=cosec^2\theta-1$

$\small \fbox\red{know \: more}</p><p>$

$\leadsto \bf cos^2\theta + {sin}^{2} \theta = 1$

$\leadsto \bf 1 + {tan}^{2} \theta = {sec}^{2} \theta$