Prove (tan x * sin x) + cos x = 1/cosx?

Question

Prove (tan x * sin x) + cos x = 1/cosx

Answer 1

Use trig identities.

(tan x * sin x) + cos x =

(sinx/cosx)* sinx + cosx =

sin^2(x)/cosx + cosx =

sin^2(x)/cosx + cos^2(x)/cosx =

[sin^2(x) + cos^s(x)]/cosx =

1/cosx

QED

.

Answer 2

Assuming we use a simple number like 5

(tan 5 * sin 5) + cos 5 = 1/cos 5

(.0874887 * .0871557) + .9961947 = 1/ .9961947

(.0076251) + .9961947 = 1.0038198

1.0038198 = 1.0038198

Answer 3

(tan x*sin x)+cos x=(sin x/cos x * sin x)+cos x= (sin x* sin x)/cos x+ cos x=(sin x^2 + cos x ^2)/cos x= 1/cos x;
sin x^2+cos x^2=1.
Hope you understand something because I don`t really know how to make them look like fractions.

Answer 4

GIVEN:
tan x * sin x + cos x

= (sin x / cos x) * sin x + cos x (i.e., tan x = sin x / cos x)

= (sin^2 x / cos x) + cos^2 x / cos x (get common denom.)

= (sin^2 x + cos^2 x) / cos x (combine terms)

= 1/cos x (PROVEN) (sin^2 x + cos^2 x = 1 by def'n)

Answer 5

(sin x/cos x*sin x)+cos x=1/cos x
sin^2x/cos x+cos x=1/cos x
cos x(sin^2x/cos x+cos x)=1/cos x
(sin^2x+cos^2)/cos x
1/cos x=1/cos x
The numerator is 1 because sin^2+cos^2=1

Answer 6

(sinx/cosx)*sinx+cosx = sin^2x/cosx+cos^2x/cosx = (sin^2x+cos^2x)/cosx=1/cosx