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: cot²P - cosec²P

Answer 1

cosP = `"PS"/"PQ" = (4)/(5)`

cot²P - cosec²P

= `("cos P"/"sin P")^2 - (1/"sin P")^2`

= `((4/5)/(3/5))^2 - (1/(3/5))^2`

= `(4/3)^2 - (5/3)^2`

= `(16)/(9) - (25)/(9)`

= `-(9)/(9)`
= -1.