Question

Cosa \div tana = 1 - sin ^{2} a \div \sqrt{1 - cos ^{2} } acosa÷tana=1−sin

2
a÷
1−cos
2

​
a
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Answer 1

Explanation:

Hey there!

LHS

`= ( \cos(a) )/( \tan(a) )`

Use tan A = sin A/cosA

`= \cos(a) * ( \cos(a) )/( \sin(a) )`

`= \frac{ { \cos(a) }^(2) }{ \sin(a) }`

Then, Use formula cos²A = 1-sin²A and sinA = √(1-cos²A)

`= \frac{1 - { \sin(a) }^(2) }{ \sqrt{ - { \cos(a) }^(2) } }`

Proved!

Hope it helps!