Question

Can I know the 25th answer step by step?

Answer 1

${ \sec}^{2} 10 - { \cot}^{2} 80 + \frac{ \sin(15) \cos(75) + \cos(15) \sin(75) }{ \cos( \beta ) \sin(90 - \beta ) + \sin( \beta ) \cos(90 - \beta ) } \\ \\ = { \sec}^{2} 10 - { \tan}^{2} (90 - 80)+ \frac{ \sin(15) \sin (90 - 75) + \cos(15) \cos(90 - 75) }{ \cos( \beta ) \sin(90 - \beta ) + \sin( \beta ) \cos(90 - \beta ) }$


$= ({ \sec}^{2} 10 - { \tan}^{2} 10)+ \frac{ \sin(15) \sin (15) + \cos(15) \cos(15) }{ \cos( \beta ) \cos( \beta ) + \sin( \beta ) \sin( \beta ) } \\ \\ =( 1) + \frac{ { \sin}^{2}( 15) + { \cos }^{2}(15) }{{ \sin}^{2}( \beta ) + { \cos }^{2}( \beta )} \\ \\ = 1 + \frac{1}{1} \\ \\ = 1 + 1 \\ \\ = 2$

Answer 2

Answer:

→ $\Huge\boxed{2}$

Step-by-step explanation:

$\begin{lgathered}{ \sec}^{2} 10 - { \cot}^{2} 80 + \frac{ \sin(15) \cos(75) + \cos(15) \sin(75) }{ \cos( \beta ) \sin(90 - \beta ) + \sin( \beta ) \cos(90 - \beta ) } \\ \\ = { \sec}^{2} 10 - { \tan}^{2} (90 - 80)+ \frac{ \sin(15) \sin (90 - 75) + \cos(15) \cos(90 - 75) }{ \cos( \beta ) \sin(90 - \beta ) + \sin( \beta ) \cos(90 - \beta ) }\end{lgathered}$

$\begin{lgathered}= ({ \sec}^{2} 10 - { \tan}^{2} 10)+ \frac{ \sin(15) \sin (15) + \cos(15) \cos(15) }{ \cos( \beta ) \cos( \beta ) + \sin( \beta ) \sin( \beta ) } \\ \\ =( 1) + \frac{ { \sin}^{2}( 15) + { \cos }^{2}(15) }{{ \sin}^{2}( \beta ) + { \cos }^{2}( \beta )} \\ \\ = 1 + \frac{1}{1} \\ \\ = 1 + 1 \\ \\ = 2\end{lgathered}$