Find the value of cosec 20° – sec 20°.

1.	Find the value of cosec 20° – sec 20°.
Answer» ☀️ Given that, we have to FIND the value of √3 COSSEC 20° - sec 20°. ⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━ T H E R E F O R E, As we KNOW that, $\bigstar \;\; \large{\underline{\boxed{ \bf cossec \theta = \dfrac{1}{sin \theta \; }}}}$ $\bigstar \;\; \large{\underline{\boxed{ \bf sec \theta = \dfrac{1}{cos \theta \; }}}}$ $\sf : \; \implies \dfrac{\sqrt{3}}{sin \; 20^{ \circ }} - \dfrac{1}{cos \; 20^{ \circ}}$ $\sf : \; \implies 2 \bigg( \dfrac{ \dfrac{\sqrt{3}}{2}}{sin \; 20^{ \circ }} - \dfrac{\dfrac{1}{2}}{cos \; 20^{ \circ}} \bigg)$ $\bigstar \;\; \large{\underline{\boxed{ \bf cos \; 30^{ \circ } = sin \; 60^{ \circ } =\dfrac{ \sqrt{3}}{2} \; }}}}$ $\sf : \; \implies 2 \bigg( \dfrac{cos\; 30^{\circ}}{sin \; 20^{ \circ }} - \dfrac{sin \; 30^{\circ}}{cos \; 20^{ \circ}} \bigg)$ $\sf : \; \implies 2 \bigg( \dfrac{cos\; 30^{\circ} \; cos\; 20^{\circ} - sin \; 30^{\circ} \; sin \; 20^{\circ}}{sin \; 20^{ \circ } \; cos \; 20^{\circ}} \bigg)$ $\bigstar \;\; \large{\underline{\boxed{ \bf (cos \; A \times cos \; B )- ( sin \; A \times sin \; B ) = cos( A + B )\; }}}}$ $\sf : \; \implies 2 \bigg( \dfrac{cos\; ( 50^{\circ}) }{sin \; 20^{ \circ } \; cos \; 20^{\circ}} \bigg)$ $\sf : \; \implies 2 \times 2 \bigg( \dfrac{cos\; ( 50^{\circ}) }{ 2 \times sin \; 20^{ \circ } \; cos \; 20^{\circ}} \bigg)$ $\bigstar \;\; \large{\underline{\boxed{ \bf 2 \times sin \; A \times cos \; A = sin ( 2A )\; }}}}$ $\sf : \; \implies <klux>4</klux> \bigg( \dfrac{cos\; ( 50^{\circ}) }{sin \; 40^{ \circ}} \bigg)$ $\sf : \; \implies 4 \bigg( \dfrac{cos\; ( 50^{\circ}) }{sin \; (90^{ \circ} - 50^{\circ})} \bigg)$ $\bigstar \;\; \large{\underline{\boxed{ \bf sin ( 90 - \theta ) = cos \theta\; }}}}$ $\sf : \; \implies 4 \bigg( \dfrac{cos\; ( 50^{\circ}) }{cos50^{\circ}} \bigg)$ $\sf : \; \implies 4 \times 1$ $\boxed{\bf{ \maltese \;\; \sqrt{3}\; cossec \; 20^{\circ} - sec\; 20^{\circ} \implies 4 }}$ ⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━ Henceforth, the value is 4. ADD to knowledge :- $\boxed{\begin{minipage}{7 cm}Fundamental Trigonometric Identities \\ \\$\sin^2\theta + \cos^2\theta=1 \\ \\1+\tan^2\theta = \sec^2\theta \\ \\1+\cot^2\theta = \text{cosec}^2 \, \theta$\end{minipage}}$ [ Note : Kindly view the answer on website brainly.in/question/43037676 ]

Answer»

☀️ Given that, we have to FIND the value of √3 COSSEC 20° - sec 20°.

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━

T H E R E F O R E,

As we KNOW that,

$\bigstar \;\; \large{\underline{\boxed{ \bf cossec \theta = \dfrac{1}{sin \theta \; }}}}$

$\bigstar \;\; \large{\underline{\boxed{ \bf sec \theta = \dfrac{1}{cos \theta \; }}}}$

$\sf : \; \implies \dfrac{\sqrt{3}}{sin \; 20^{ \circ }} - \dfrac{1}{cos \; 20^{ \circ}}$

$\sf : \; \implies 2 \bigg( \dfrac{ \dfrac{\sqrt{3}}{2}}{sin \; 20^{ \circ }} - \dfrac{\dfrac{1}{2}}{cos \; 20^{ \circ}} \bigg)$

$\bigstar \;\; \large{\underline{\boxed{ \bf cos \; 30^{ \circ } = sin \; 60^{ \circ } =\dfrac{ \sqrt{3}}{2} \; }}}}$

$\sf : \; \implies 2 \bigg( \dfrac{cos\; 30^{\circ}}{sin \; 20^{ \circ }} - \dfrac{sin \; 30^{\circ}}{cos \; 20^{ \circ}} \bigg)$

$\sf : \; \implies 2 \bigg( \dfrac{cos\; 30^{\circ} \; cos\; 20^{\circ} - sin \; 30^{\circ} \; sin \; 20^{\circ}}{sin \; 20^{ \circ } \; cos \; 20^{\circ}} \bigg)$

$\bigstar \;\; \large{\underline{\boxed{ \bf (cos \; A \times cos \; B )- ( sin \; A \times sin \; B ) = cos( A + B )\; }}}}$

$\sf : \; \implies 2 \bigg( \dfrac{cos\; ( 50^{\circ}) }{sin \; 20^{ \circ } \; cos \; 20^{\circ}} \bigg)$

$\sf : \; \implies 2 \times 2 \bigg( \dfrac{cos\; ( 50^{\circ}) }{ 2 \times sin \; 20^{ \circ } \; cos \; 20^{\circ}} \bigg)$

$\bigstar \;\; \large{\underline{\boxed{ \bf 2 \times sin \; A \times cos \; A = sin ( 2A )\; }}}}$

$\sf : \; \implies <klux>4</klux> \bigg( \dfrac{cos\; ( 50^{\circ}) }{sin \; 40^{ \circ}} \bigg)$

$\sf : \; \implies 4 \bigg( \dfrac{cos\; ( 50^{\circ}) }{sin \; (90^{ \circ} - 50^{\circ})} \bigg)$

$\bigstar \;\; \large{\underline{\boxed{ \bf sin ( 90 - \theta ) = cos \theta\; }}}}$

$\sf : \; \implies 4 \bigg( \dfrac{cos\; ( 50^{\circ}) }{cos50^{\circ}} \bigg)$

$\sf : \; \implies 4 \times 1$

$\boxed{\bf{ \maltese \;\; \sqrt{3}\; cossec \; 20^{\circ} - sec\; 20^{\circ} \implies 4 }}$

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━

Henceforth, the value is 4.

ADD to knowledge :-

$\boxed{\begin{minipage}{7 cm}Fundamental Trigonometric Identities \\ \\$\sin^2\theta + \cos^2\theta=1 \\ \\1+\tan^2\theta = \sec^2\theta \\ \\1+\cot^2\theta = \text{cosec}^2 \, \theta$\end{minipage}}$

[ Note : Kindly view the answer on website brainly.in/question/43037676 ]