Prove that 1 - A A - sin 2 A 1 - cos A-

1+ A A=sin^2 A1 cos A cos A+1cos A×cos A=cos A+1×(1 cos A)1 cos A=1 cos^2A1 cos A ⇒sin^2A1 cos A . ...

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Trigonometric Ratios

Prove that ...

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Prove that $\frac{1 + sec A}{sec A} = \frac{{sin}^{2} A}{1 - cos A}$ .

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\sqrt{\frac{1 + sin 2 A}{1 - sin 2 A}} = tan (\frac{π}{4} + A) .

\frac{tan A}{1 - cot A} + \frac{cos A}{1 - tan A} = 1 + tan A + cot A = 1 + sec A csc A

Prove that:
1. $\sqrt{s e c^{2} A + c o s e c^{2} A}$ = tanA + cotA

2. $s i n^{2} A (1 + c o t^{2} A) + c o s^{2} A (1 + t a n^{2} A)$ = 2

\sqrt{\frac{1 - c o s A}{1 + c o s A}} + \sqrt{\frac{1 + c o s A}{1 - c o s A}} = 2 c o s e c A

\frac{1 + cos A + sin A}{1 + cos A - sin A} = \frac{1 + sinA}{cos A}

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