Verify: tan^2 x/secx = sinx tanx?

1). tan^2 x/secx = sinx tanx

(sin²x / cos²x)/(1/cosx)=sinx*(sinx)/(cosx)=

sinx tanx

1) tan^2 x = sin^2 x / cos^2 x

=> tan^2x/secx = (sin^2 x/cos^2 x)/secx (secx = 1/cosx)

= (sin^2 x * cosx)/cos^2 x [cancel cosx with cosx]

= sin^2x/cosx

= (sinx * sinx)/cosx

= tanx sinx or sinx tanx [sinx/cosx = tanx]

Hope this helps :)

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

Simplifying the LHS:

(sec^2(x) - 1)/sec(x) = sec(x) - cos(x) = sin²(x)/cos(x) = tan(x)*sin(x)