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प्रश्न
Prove the following trigonometric identities.
`(1 + cos A)/sin A = sin A/(1 - cos A)`
उत्तर
We need to prove `(1 + cos A)/sin A = sin A/(1 - cos A)`
Now, multiplying the numerator and denominator of LHS by `1 - cos A` we get
`(1 + cos A)/sin A = (1 + cos A)/sin A xx (1 - cos A)/(1 - cos A)`
Further using the identity, `a^2 - b^2 = (a + b)(a - b)` we get
`(1 + cos A)/sin A xx (1 - cos A)/(1 - cos A) = (1 - cos^2 A)/(sin A (1- cos A))`
`= sin^2 A/(sin A(1 - cos A))` (Using `sin^2 theta + cos^2 theta = 1`)
`= sin A/(1 - cos A)`
Hence proved
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