Question

verify:
cosx + sinxtanx = secx

Answer 1

first, convert tanx to sinx/cosx

Answer 2

left side be :
cosx + sinx*sinx/cosx or
cos^2/cosx + sin^2 x/cosx

Answer 3

because the denominator has same, just adding the numerator :
(cos^2 x + sin^2 x)/cosx

Answer 4

remember the identity :
sin^2 x + cos^2 x = 1,
so, it can be :
(cos^2 x + sin^2 x)/cosx = 1/cosx

Answer 5

and finally, use the identity that 1/cosx = secx

Answer 6

thank you so much!!

Answer 7

LHS = RHS
you're welcome