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3 years ago

CosA/1-sinA=1+sinA/cosA

Mathematics

1 answer:

Triss [41]3 years ago

7 0

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identity

sin²x + cos²x = 1 ⇒ cos²x = 1 - sin²x

Consider the left side

$\frac{cosA}{1-sinA}$ ← multiply numerator/denominator by (1 + sinA)

= $\frac{cosA(1+sinA)}{(1-sinA)(1+sinA)}$ ← expand denominator using FOIL

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

= $\frac{cosA(1+sinA)}{cos^2A}$ ← cancel cosA on numerator/ denominator

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

= right side , thus proven

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CosA/1-sinA=1+sinA/cosA​

CosA/1-sinA=1+sinA/cosA