From algebra we know that if `ax^(2) +bx + c=0 , a( ne 0), b, c int R` has roots `alpha` and `beta` then `alpha + beta=-b/a` and `alpha beta = c/a`. Trignometric functions `sin theta` and `cos theta, tan theta` and `sec theta, " cosec " theta` and `cot theta` obey `sin^(2)theta + cos^(2)theta =1`. A linear relation in `sin theta` and `cos theta, sec theta` and `tan theta` or `" cosec "theta` and `cos theta` can be transformed into a quadratic equation in, say, `sin theta, tan theta` or `cot theta` respectively. And then one can apply sum and product of roots to find the desired result. Let `a cos theta, b sintheta=c` have two roots `theta_(1)` and `theta_(2)`. `theta_(1) ne theta_(2)`.
The values of `tan theta_(1) tan theta_(2)` is (given `|b| ne |c|)`

Options

A. `(a^(2)-c^(2))/(a^(2)+b^(2))`
B. `(a^(2)+c^(2))/(a^(2)+b^(2))`
C. `(a^(2)-c^(2))/(c^(2)-b^(2))`
D. `(c^(2)-a^(2))/(c^(2)-b^(2))`

Answer

D