Question

Sec^2(105+alpha)-tan^2(75-alpha) solve mathematicaly

Answer 1

Answer:

$\boxed{ \huge \pink{1}}$

Step-by-step explanation:

$\bold{\underline{ \red{to \: find}}} \longrightarrow \\ value \: of \\ {sec}^{2} (105 + \alpha ) - {tan}^{2} (75 - \alpha )$

$\bold{ \underline{ \green{concept \: used}}} \longrightarrow \\ \boxed{ \pink{ \large{sec(180 - \theta ) = - sec \theta}}} \\ \boxed{ \blue{ \large{ {sec}^{2} \theta - {tan}^{2} \theta = 1}}}$

$\bold{ \underline{ \orange{solution}}} \longrightarrow \\ {sec}^{2} (105 + \alpha ) - {tan}^{2} (75 - \alpha ) \\ = {sec}^{2} (180 - 75 + \alpha ) - {tan}^{2} (75 - \alpha ) \\ = {sec}^{2} (180 - (75 - \alpha )) - {tan}^{2} (75 - \alpha ) \\ = ({ sec(180 - (75 - \alpha ))}^{2} - {tan}^{2} (75 - \alpha ) \\ = ( - sec(75 - \alpha )) ^{2} - {tan}^{2} (75 - \alpha ) \\ = {sec}^{2} (75 - \alpha ) - {tan}^{2} (75 - \alpha ) \\ = 1$