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According to Pythagoras theorem, PR2 = PQ2 + QR2 PQ2 = PR2 - QR2 PQ2 = (√x+3)2 - (√7)2 PQ2 = (x + 3) - (7) PQ2 = (x - 4) PQ = √(x - 4) tan P = √7 / √(x - 4) sin R = √(x - 4) / √(x + 3) cosec P = √(x + 3) / √7 cos 90° = 0 cot2 P = (x - 4) / 7 cosec Q = 1 tan P. sin R. cosec P - cos Q + 7 cot2 P. cosec Q = [√7 / √(x - 4)] x [√(x - 4) / √(x + 3)] x [√(x + 3) / √7] - [0] + 7 [(x - 4) / 7] x [1] = 1 - 0 + (x - 4) = 1 - 0 + x - 4 = (x - 3) Therefore, the value of tan P. sin R. cosec P - cos Q + 7 cot2 P. cosec Q is (x - 3).
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