Question

plssss help guys ...... tell the answer

Answer 1

Here is the answer :

Formulas We need :
(1) Sin² A + Cos² A = 1,
(2) Sec A = 1/Cos A, Cosec A = 1/Sin A,

For my Convenience I am considering theta as A, and Cosec as Csc

=>
$\sqrt{ {sec}^{2} \: a+ {csc}^{2} \: a}$
=>
$\sqrt{ ({ \frac{1}{cos \: a}) }^{2} + ({ \frac{1}{sin \: a} }^{2}) }$
=>
$\sqrt{ \frac{( {cos \: a) }^{2} + ({sin \: a})^{2} }{( {cos \: a})^{2} \times ( {sin \: a \: )}^{2} } }$
=>
$\frac{1}{cos \: a \: \times \: sin \: a}$

We know that,
${cos \:}^{2} \: a \: + \: {sin}^{2} \: a \: \: = \: 1$

=>
$\frac{ {sin}^{2} \: a \: + \: {cos}^{2} \: a}{sin \: a \: \times \: cos \: a \: }$
=>
$\frac{ {sin}^{2} \: a }{sin \: a \: \times \: cos \: a} \: + \: \frac{ {cos}^{2} \: a }{sin \: a \: \times \: cos \: a}$
=>
$\frac{sin \: a \: }{cos \: a \: } + \: \frac{cos \: a \: }{sin \: a}$

=>
$tan \: a \: + \: cot \: a$

Therefore : Hence Proved !!

Hope you understand, Have a Great day :D,
Thanking you, Bunti 360 !..