Question

How to solve Prove Trigonometry Questions?


Example Question:-

(1 - sin A)/(1 + sin A) = (sec A - tan A)2


Please give answer maths experts

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Answer 1

Step-by-step explanation:

Given :-

(1 - sin A)/(1 + sin A)

To find :-

Prove that :(1 - sin A)/(1 + sin A) = (sec A - tan A)²

Solution :-

On taking LHS :

(1 - sin A)/(1 + sin A)

On multiplying both the numerator and the denominator with (1-Sin A) then

=>[(1 - sin A)/(1 + sin A)]×[(1 - sin A)/(1 - sin A)]

=> [(1 - sin A)(1 - sin A)]/ [(1 +sin A)(1 - sin A)]

=> (1 - sin A)²/ [(1 +sin A)(1 - sin A)]

=> (1 - sin A)²/ (1²-sin² A)

Since (a+b)(a-b) = a²-b²

Where, a = 1 and b = Sin A

=> (1 - sin A)²/ (1-sin² A)

We know that

Sin² A + Cos² A = 1

=>(1 - sin A)²/ Cos² A

=> [(1-Sin A)/Cos A]²

=> [(1/Cos A) -(Sin A/Cos A)]²

=> (Sec A - Tan A)²

=> RHS

=> LHS = RHS

Hence, Proved.

Answer:-

(1 - sin A)/(1 + sin A) = (sec A - tan A)²

Used formulae:-

→ (a+b)(a-b) = a²-b²

→ Sin² A + Cos² A = 1

→ Sec A = 1/Cos A

→ Tan A = Sin A / Cos A