Question

Prove
Sin A/1+cos A=1-cos A/ Sin A​

Answer 1

Answer:

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..To prove,

....sinA/1+cosA=1-cosA/sinA

L.H.S=sinA/1+cosA

rationalise the denominator of the L. H. s..

sinA×(1—cosA)/(1+cosA)×(1—cosA)

using the property (a+b)(a–b) =a²–b²

sinA(1—cosA) /(1)²—(cos)²

sinA(1—cosA) /(1—cos²A)

using the property (1–cos²A) =sin²A

sinA(1—cos A) /Sin²A

SinA(1—cosA) /sinA×sinA

(1—cosA) /sinA=L.H.S....... proved...

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Answer 2

Answer:

• $\frac{sinA}{1+cosA}=\frac{1-cosA}{sinA}$

Step-by-step explanation:

L.H.S

$\\ \frac{sinA}{1+cosA} \\\\=>\frac{sinA}{1+cosA}.\frac{1-cosA}{1-cosA}\\\\ =>\frac{sinA(1-cosA)}{(1+cosA)(1-cosA)}\\\\ =>\frac{sinA(1-cosA)}{1-cos^2A}\\\\ =>\frac{sinA(1-cosA)}{sin^2A}\\\\ =>\frac{1-cosA}{sinA}$

R.H.S

Hence Proved.

The method we use here is rationalization.

and use some trigonometric formulas