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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
Solution
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.
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