Question

tan (x) sin (x) + cos (x) = sec (x)​

Answer 1

sinx/cosx*sinx + cosx

=sinx/cosx*sinx + cos²x

=now sinx +cos²x= sec*cosx

=sin²x + cos²x = 1/cosx *cosx

=sin²x +cos²x =1

LHS = RHS

Answer 2

Answer:

sin²x +cos²x =1

Step-by-step explanation:

$< > \: \tan = \frac{ \sin }{ \cos } put \: it \: in \: \tan \\ \\ = > \frac{ \sin }{ \cos } \times \sin(x) + { \cos(x) }^{2} = \sec(x) \\ \\ = > \sin(x) + { \cos(x) }^{2} = \sin(x) \times \cos(x) \\ \\ = > { \sin(x) }^{2} + { \cos(x) }^{2} = 1$