Question

Prove "sec(1-sinA) (secA+tanA)=1

Answer 1

Answer:

Hola ‼........❤

LHS = SecA(1-SinA) (SecA+TanA)

= (1/CosA) (1-SinA) (1/CosA + SinA/CosA)

= (1-SinA/CosA) (1+SinA/CosA)

= (1- SinA) (1+SinA)/ Cos²A

= 1-Sin²A/Cos²A [using (a+b)(a-b) =a²-

b²]

=Cos²A/Cos²A [using 1- Sin²A= Cos²A]

= 1 = RHS

Hope it's helpful........ ☺

Answer 2

Step-by-step explanation:

LHS:

SecA(1-SinA) (SecA+TanA)

=> (1/CosA) (1-SinA) (1/CosA + SinA/CosA)

=> (1-SinA/CosA) (1+SinA/CosA)

=> (1- SinA) (1+SinA)/ Cos²A

=> 1-Sin²A/Cos²A [using (a+b)(a-b) =a²-b²]

=>Cos²A/Cos²A [using 1- Sin²A = Cos²A]

=> 1 = RHS [PROVED]