Prove that- 1-tan A- Asin A-cos A-sin Atan A- Acos A

Now, (1+tan A+ A)(sin A cos A) = (sin A cos A)+(tan A.sin A cos A.tan A)+( A.sin A Acos #160; A) = (sin A cos A)+(tan A.sin A sin A)+ ...

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Tangent, Cotangent, Secant, Cosecant in Terms of Sine and Cosine

Prove that: ...

Question

Prove that:
$(1 + tan A + cot A) (sin A - cos A) = sin A tan A - cot A cos A$

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(1 + cot A + tan A) (sin A - cos A) = sin A tan A - cot A cos A

(1 + \cot A + \tan A) (\sin A - \cos A) = \frac{\sec A}{{cosec}^{2} A} - \frac{cosec A}{\sec^{2} A} = \sin A \tan A - \cot A \cos A

Prove the following identities:

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

(1 + cot A + tan A) (sin A - cos A) = \frac{sec A}{{cosec}^{2} A} - \frac{cosec A}{{sec}^{2} A} = sin A tan A - cot A cos A

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