Prove the following trigonometric identities (secx+tanx)(1-sinx/cosx)=1

Below.

Step-by-step explanation:

Convert  to sin's and cos's:-

(secx + tanx)(1-sinx)/cosx)

= ( 1/ cos x + sinx / cos x) * ( 1 - sin x )/ cos x)

=  (1 + sin x) / cos x) *  ( 1 - sin x ) / cos x

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

But 1 - sin^2 x = cos^2 x

so we have

cos^2 x / cos^2 x  which = 1.

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)