Prove that:- (1-sinA)(1+sinA)÷(1+cosA)(1-cosA)=cot^2A

Mathematics

1 answer:

astraxan [27]3 years ago

6 0

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identity

sin²x + cos²x = 1 , then

sin²x = 1 - cos²x and cos²x = 1 - sin²x

Consider the left side

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

= $\frac{1-sin^2A}{1-cos^2A}$

= $\frac{1-(1-cos^2A)}{1-(1-sin^2A)}$

= $\frac{1-1+cos^2A}{1-1+sin^2A}$

= $\frac{cos^2A}{sin^2A}$

= cot²A = right side , thus proven

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