Prove that sin2A - 11 - tan2A - 1-

Identites : #160; sin ^2A+cos ^2A=1 LHS = sin ^2A+11+tan^2A #160; #160; #160; #160; #160; =sin ^2A+1 ^2A #160; #160; #160 ...

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Trigonometric Identities

Prove that ...

Question

Prove that ${sin}^{2} A + \frac{1}{1 + {tan}^{2} A} = 1$ .

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(1 + \frac{1}{{tan}^{2} A}) \times (1 + \frac{1}{{cot}^{2} A}) = \frac{1}{{sin}^{2} A - {sin}^{4} A}

\frac{{cos}^{2} A + {tan}^{2} A - 1}{{sin}^{2} A} = {tan}^{2} A .

(1 + {tan}^{2} A) (1 + \frac{1}{{tan}^{2} A}) = \frac{1}{{sin}^{2} A - {sin}^{4} A}

Prove the following trigonometric identities:

$(1 + t a n^{2} A) + (1 + \frac{1}{t a n^{2} A}) = \frac{1}{s i n^{2} A - s i n^{4} A}$

How many of below given statements are correct?

1. sin2A = 2sinA.cosA

2.cos2A = $s i n^{2} A - c o s^{2} A$

3.tan A = $\frac{2 t a n \frac{A}{2}}{1 - t a n^{2} \frac{A}{2}}$

4. $s i n^{2} \frac{A}{2}$ = 1 - cosA

5. $t a n^{2} A$ = $\frac{1 - c o s 2 A}{1 + c o s 2 A}$

6. $s i n^{2} A$ = $\frac{2 t a n A}{1 - t a n^{2} A}$

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