Question

✌❤ ₱røve it ......✌❤​

Answer 1

Correct Question :

$\frac{ \sec \theta}{ \cosec \theta} + \frac{ \cosec \theta}{ \sec \theta } = \sec \theta . \cosec \theta.$

Solution :

Taking LHS,

$\leadsto\frac{ \sec \theta}{ \cosec \theta} + \frac{ \cosec \theta}{ \sec \theta }$

$\leadsto \frac{ \frac{1}{ \cos \theta } }{ \frac{1}{ \sin \theta} } + \frac{ \frac{1}{ \sin\theta } }{ \frac{1}{ \cos \theta} }$

$\leadsto \frac{ \sin \theta }{ \cos \theta} + \frac{ \cos \theta}{ \sin \theta}$

$\leadsto \frac{ { \sin }^{2} \theta + {\cos }^{2} \theta}{ \sin \theta . \cos \theta}$

$\leadsto \frac{1}{ \sin \theta. \cos \theta }$

$\leadsto \sec \theta. \cosec \theta.$

Hence, LHS = RHS.

$\\ \rule{200}3$

Some identities.

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