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Brilliant_brown [7]
3 years ago
5

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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