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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: 4sin2R - `(1)/("tan"^2"P")`
Solution
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)`.
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