Prove that : ( 1+Cot A +Tan A)(Sin A - Cos A) = Sec Aplease its really

1.	Prove that : ( 1+Cot A +Tan A)(Sin A - Cos A) = Sec Aplease its really urgent
Answer» Step-by-step EXPLANATION: Let L.H.S= (1+cotA+tanA)(sinA−cosA) =(1+ SINACOSA + cosAsinA)(sinA−cosA) =( sinAcosAsinAcosA+cos 2 A+sin 2 A ) (Sina−cosA) =(1+sinAcosA)(sinAcosAsinA−cosA) Now, R.H.S=sinAtanA−cotAcosA =sinA cosAsinA − sinAcosAcosA= cosAsin2A − sinAcos 2 A= sinAcosAsin 2A−cos3 A= sinAcosA(sinA−cosA) (SIN2 A+cos2A+sinAcosA)=(1+sinAcosA) sinAcosA(sinA−cosA) Hence, L.H.S=R.H.S proved

Prove that : ( 1+Cot A +Tan A)(Sin A - Cos A) = Sec Aplease its really urgent

Answer»

Step-by-step EXPLANATION:

Let

L.H.S= (1+cotA+tanA)(sinA−cosA)

=(1+

SINACOSA + cosAsinA)(sinA−cosA) =( sinAcosAsinAcosA+cos 2 A+sin 2 A )

(Sina−cosA)

=(1+sinAcosA)(sinAcosAsinA−cosA)

Now,

R.H.S=sinAtanA−cotAcosA

=sinA cosAsinA − sinAcosAcosA= cosAsin2A −

sinAcos 2

A= sinAcosAsin 2A−cos3 A= sinAcosA(sinA−cosA)

(SIN2 A+cos2A+sinAcosA)=(1+sinAcosA) sinAcosA(sinA−cosA)

Hence,

L.H.S=R.H.S

proved