Question

Solve (ii) (sec A + tan A) (1 - sin A) ​

Answer 1

Step-by-step explanation:

Given :-

(Sec A + Tan A) ( 1- Sin A)

To find :-

Simplify the expression ?

Solution :-

Given that

(Sec A + Tan A) ( 1- Sin A)

=> [(1/Cos A) + (Sin A/ Cos A )] (1-Sin A)

=>[ (1+Sin A )/Cos A ](1-Sin A)

=> (1+Sin A)(1-Sin A)/Cos A

=> (1²-Sin²A)/(Cos A)

Since (a+b)(a-b) = a²-b²

=> (1-Sin² A )/Cos A

We know that

Sin² A + Cos² A = 1

=> Cos² A/Cos A

=> (Cos A ×Cos A)/Cos A

=> Cos A

Answer:-

(Sec A + Tan A) ( 1- Sin A) = Cos A

Used Identities:-

→ Sec A = 1/ Cos A

→ Tan A = Sin A / Cos A

→ Sin² A + Cos² A = 1

→ (a+b)(a-b) = a²-b²