Question

Prove that: `(cos e c(90^0+theta)+cot(450^0+theta))/(cos e c(90^0-theta)+t a n(180^0-theta))+(t a n(180^0+theta)+s e c(180^0-theta))/(t a n(360^0+theta)-s e c(-theta))`=2

Answer 1

`L.H.S. = (cosec(90^@+theta)+cot(450^@+theta))/(cosec(90^@-theta)+tan(180^@-theta))+(tan(180^@+theta)+sec(180^@-theta))/(tan(360^@+theta)-sec(-theta)`
`=(cosec(90^@+theta)+cot(360^@+90^@+theta))/(cosec(90^@-theta)+tan(180^@-theta))+(tan(180^@+theta)+sec(180^@-theta))/(tan(360^@+theta)-sec(theta)`
`=(cosec(90^@+theta)+cot(90^@+theta))/(cosec(90^@-theta)+tan(180^@-theta))+(tan(180^@+theta)+sec(180^@-theta))/(tan(360^@+theta)-sec(theta)`
`=(sec(theta)-tan(theta))/(sec(theta)-tan(theta))+(tan(theta)-sec(theta))/(tan(theta)-sec(theta)`
`1+1 = 2= R.H.S.`