Prove the identity- sin 2 A -cos 2 A -cos 2 A -sin 2 A -1-sin 2 A cos 2 A -2-4 MARKS -

Formula: 2 Marks Proof: 2 Marks sin^2 A/cos^2 A+cos^2 A/sin^2 A=1/sin^2 A cos^2 A 2 ⇒sin^2 A/cos^2 A+cos^2 A/sin^2 A=1/sin^2 A cos^2 A ⇒sin^2 A/cos^2 A+cos^2 ...

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Standard XII

Chemistry

Introduction to Haloalkanes

Prove the ide...

Question

Prove the identity: $\frac{s i n^{2} A}{c o s^{2} A} + \frac{c o s^{2} A}{s i n^{2} A} = \frac{1}{s i n^{2} A c o s^{2} A} - 2$ [4 MARKS]

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Solution

Formula: 2 Marks
Proof: 2 Marks

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

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Prove the identity:sin2 Acos2 A+cos2 Asin2 A=1sin2 A cos2 A−2 [4 MARKS]

Prove the identity: $\frac{s i n^{2} A}{c o s^{2} A} + \frac{c o s^{2} A}{s i n^{2} A} = \frac{1}{s i n^{2} A c o s^{2} A} - 2$ [4 MARKS]