Question

prove that tan^2A+cot^2A=sec^2Acosec^2A-2​

Answer 1

Answer:

$tan^{2}A+cot^{2}A=sec^{2}Acosec^{2}A-2\\=$

Step-by-step explanation:

$LHS = tan^{2}A+cot^{2}A\\=sec^{2}A-1+cosec^{2}A-1\\=sec^{2}A+cosec^{2}A-2\\=\frac{1}{cos^{2}A}+\frac{1}{sin^{2}A}-2\\=[\frac{sin^{2}A+cos^{2}A}{cos^{2}Asin^{2}A}]-2\\=\frac{1}{cos^{2}Asin^{2}A}-2\\=sec^{2}Acosec^{2}A-2\\=RHS$

Therefore,

$tan^{2}A+cot^{2}A=sec^{2}Acosec^{2}A-2\\=$

•••♪