Question

Prove that : 1/1-secA + 1/1+secA = -2cot^2A​

Answer 1

Answer:

Step-by-step explanation:

LHS = 1/1-secA + 1/1+secA

       $= \frac{1*(1+Sec A)}{(1-Sec A)(1+Sec A)}+\frac{1*(1-Sec A)}{(1+Sec A)*(1-Sec A)}\\\\=\frac{(1+Sec A)}{1-Sec^{2} A}+\frac{(1-Sec A)}{1-Sec^{2} A}\\\\=\frac{1+Sec A+1-Sec A}{(1-Sec^{2} A)}\\\\= \frac{2}{(1-Sec^{2} A)}\\\\=\frac{2}{-(Sec^{2} A - 1)}\\\\= \frac{-2}{Tan^{2} A}\\\\= -2Cot^{2} A$