Question

In the given figure, PQR is a triangle, in which QS ⊥ PR, QS = 3 cm, PS = 4 cm and QR = 12 cm, find the value of: 4sin²R - `(1)/("tan"^2"P")`

Answer 1

sin R = `"QS"/"QR" = (3)/(12)`

4sin²R - `(1)/("tan"^2"P")`

= 4sin²R - cot²P

= `4 xx (3/12)^2 - ("cos P"/"sin P")^2`

= `4 xx (9)/(144) - ((4/5)/(3/5))^2`

= `(9)/(36) - (16)/(9)`

= `-(55)/(36)`.