Question

Prove that:
cot0 /cosec 0 +1
+ cosec 0+1/ cot0
= 2sec0​

Answer 1

$\frac{ \cot \alpha }{ \csc \alpha + 1 } + \frac{ \csc \alpha + 1 }{ \cot \alpha } \\ \\ = > \frac{ { \cot }^{2} \alpha + {( \csc \alpha + 1) }^{2} }{ \cot \alpha ( \csc \alpha + 1) } \\ \\ = > \frac{ { \cot}^{2} \alpha + { \csc}^{2} \alpha + 1 + 2 \csc\alpha }{ \cot\alpha \csc\alpha + \cot \alpha } \\ \\ = > \frac{2 { \csc }^{2} \alpha + 2 \csc\alpha }{ \cot \alpha ( \csc\alpha + 1) } \\ \\ = > \frac{2 \csc\alpha( \csc \alpha + 1) }{ \cot\alpha ( \csc \alpha + 1) } \\ \\ = > \frac{2 \csc \alpha }{ \cot \alpha } = \frac{ \frac{2}{ \sin \alpha } }{ \frac{ \cos \alpha }{ \sin\alpha } } \\ \\ = > \frac{2}{ \cos \alpha } = 2 \sec\alpha$

{ Here, cosec²A = 1+cot²A }

HENCE PROVED

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