Question

Prove that sec x - cos x = sin x tan x

Answer 1

Answer:

put secx=1/cosx and take LCM

(1/cosx)-cosx=1-cos^2x/cosx

=sin^2x/cosx

=(sinx×sinx)/cosx

=sinx×tanx....

hence proved

Answer 2

Step-by-step explanation:

1. RHS : sec x - cos x

we know that Sec is inverse of cos.

Replacing sec with 1/cosx

2. 1/cos x - cos x

LCM is cos x

3. (1 - cos x × cos x) / cos x

4. (1 - cos ^ x)/cos x [ Cos ^ x is cos sq. x]

5. sin^x / cos x (since 1-cos^x = sin^x)

6. (sin x × sin x )/ cos x

since Sin x/cos x = tan x

replacing

tanx sin x = RHS