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Derivative of Some Standard Functions

Prove the fol...

Question

Prove the following identity where the angle involved is acute for which the expression is defined :

((1 + cotA)/ secA ) + (sin²A/ (1 - cosA))

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Solution

The given “expression” is not an “identity”. Please check the question again and upload it as a new post...

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Q. Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

\frac{cos A}{1 + sin A} + \frac{1 + sin A}{cos A} = 2 sec A

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Q. Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

\frac{(1 + s e c A)}{s e c A} = \frac{s i n^{2} A}{(1 - c o s A)}

[Hint : Simplify L.H.S and R.H.S separately]

Q. Question 5 (iv)
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
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\frac{(1 + s e c A)}{s e c A} = \frac{s i n^{2} A}{(1 - c o s A)}

[Hint : Simplify L.H.S and R.H.S separately]

Q. Prove the following identities , where the angles involved are acute angles for which the expressions are defined .
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{(c o s e c θ - c o t θ)}^{2} = \frac{1 - c o s θ}{1 + c o s θ}

\frac{c o s A}{1 + s i n A} + \frac{1 + s i n A}{c o s A} = 2 s e c A

Q. Question 5 (viii)
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
(viii)

(s i n A + c o s e c A)^{2} + (c o s A + s e c A)^{2} = 7 + t a n^{2} A + c o t^{2} A

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