Question

Prove that tan2A +cot2A +2=cosec2A sec2A

Answer 1

Answer:

$tan^{2}A+cot^{2}A+2=sec^{2}A cosec^{2}A$

Step-by-step explanation:

$LHS = tan^{2}A+cot^{2}A+2\\=(1+tan^{2}A) + (1+cot^{2}A)\\=sec^{2}A+cosec^{2}A\\=\frac{1}{cos^{2}A}+\frac{1}{cosec^{2}A}\\=\frac{sin^{2}A+cos^{2}A}{cos^{2}Asin^{2}A}\\=\frac{1}{cos^{2}Asin^{2}A}\\=sec^{2}A cosec^{2}A\\=RHS$

Therefore,

$tan^{2}A+cot^{2}A+2=sec^{2}A cosec^{2}A$

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Answer 2

Answer:

Hello friends this is your answer hope it helps you