Question

cot²thitaa - tan² thitaa = cosec2thita prove it​

Answer 1

$The \: \: question \: \: is \: \: wrong. \\ cot^{2} \theta - tan^{2} \theta \: ≠cosec2 \theta$

Step-by-step explanation:

$LSH = \: cot^{2} \theta - tan ^{2} \theta \\ = \frac{1}{tan ^{2} \theta } - tan ^{2} \theta \\ = \frac{1 -tan ^{4} \theta }{tan ^{2} \theta } \\ = \frac{(1 + tan ^{2} \theta )(1 -tan ^{2} \theta )}{tan ^{2} \theta } \\ = \frac{1 + tan ^{2} \theta}{tan \theta} \times \frac{1 - tan ^{2} \theta}{tan \theta} \\ = 4 \times( \frac{1 + tan ^{2} \theta}{2tan \theta} ) \times( \frac{1 - tan ^{2} \theta}{2tan \theta}) \\ = 4 \times \frac{1}{sin2 \theta} \times \frac{1}{tan2 \theta} \\ = \frac{4cosec 2\theta}{tan2 \theta} ≠RHS$