Question

prove that 1/1+sin2q+1/1+cos2q+1/1+sec2q+1/1+cosec2q=2​

Answer 1

Answer:

$\frac{1}{1+sin^2\theta}+\frac{1}{1+cos^2\theta}+\frac{1}{1+sec^2\theta}+\frac{1}{1+cosec^2\theta}=2$

Step-by-step explanation:

$\frac{1}{1+sin^2\theta}+\frac{1}{1+cos^2\theta}+\frac{1}{1+sec^2\theta}+\frac{1}{1+cosec^2\theta}\\\\=\frac{1}{1+sin^2\theta}+\frac{1}{1+cos^2\theta}+\frac{1}{1+\frac{1}{cos^2\theta}}+\frac{1}{1+\frac{1}{sin^2\theta}}$

$=\frac{1}{1+sin^2\theta}+\frac{sin^2\theta}{1+sin^2\theta}+\frac{1}{1+cos^2\theta}+\frac{cos^2\theta}{1+cos^2\theta}\\\\=\frac{1+sin^2\theta}{1+sin^2\theta}+\frac{1+cos^2\theta}{1+cos^2\theta}$

$=1+1\\\\=2$