Question

if cotø=7/8 evaluate (1+sinø)(1-sinø)/(1+cosø)(1-cosø)​

Answer 1

Answer:

cotθ=7/8

AB/BC = 7k/8k

In ΔABC,

AC² = AB² + BC²

AC² = (7k)² + (8k)²

AC² = 49k² + 64k²

AC² = 113k²

AC = √113k²

AC = √113 k

sinθ = AB/AC = 8k/√113 k = 8/√113

cosθ = BC/AC = 7k/√113k = 7/√113

Therefore,

=(1+sinθ)(1-sinθ)/(1+cosθ)(1-cosθ)

=(1+ 8/√113)(1-8/√113) / (1+7/√113)(1-7/√113)

=(1-64/113) / (1-49/113)

=(113-64/113)(113-49/113)

=64/49