What is the answer to this? Cosx + Sinx * Tanx = Secx?

Answer 1

cos(x) +sin(x)tan(x)=sec(x)
multiply by cos(x) on both sides
cos^2(x)+sin^2(x)=1
1=1
I believe they are probably asking you to prove the identity

Answer 2

Cosx + Sinx * Tanx = Secx
cos x+sin^2 x/cos x=1/cos x multiply by cos x
cos^2 x+sin^ x=1
1=1

it is an identity

Answer 3

the question is to be taken as
prove that cosx+sinx*tanx= secx

cosx+sinx*tanx
= cosx+sinx*(sinx/cosx)
mutiplying each term by cos x
=(cosx*cosx+sinx*sinx)/cosx
=1/cosx
since cosx*cosx+sinx*sinx
=(cos^2x+sin^2x) = 1
and by definition
1/cosx = secx

Answer 4

cos x +sinx *tan x =sec x
cos x +sin x *sin x/cos x = 1/ cos x
cos^2 x +sin^2 x =1
1=1

Answer 5

cos(x) + sin(x)tan(x) = sec(x)
cos(x) + (sin(x) * sin(x)/cos(x)) = sec(x)
cos(x) + (sin(x)^2/cos(x)) = sec(x)
(cos(x)^2 + sin(x)^2)/(cos(x)) = sec(x)

cos(x)^2 + sin(x)^2 = 1

1/(cos(x)) = sec(x)

so

sec(x) = sec(x)