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If 3 cotA= 6 sec B = -2√10Where π/2 < A< π and π < B < 3π/2Evaluate cosecA - tanB |
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Answer» Step-by-step explanation: We KNOW: sin 2 x + cos 2 x = 1 , THEREFORE, sin x = √ 1 − cos 2 x
sin θ = ± √ 1 − ( 8 13 ) 2 = ± √ 1 − 64 169 = ± √ 169 − 64 169 sin θ = ± √ 105 169 = ± √ 105 13
But because θ is between 3 π 2 and 2 π , i.e in the third QUADRANT, sin θ = − √ 105 13
sin 2 θ = 2 sin θ cos θ = 2 ( √ 105 13 ) ( 8 13 ) = 16 √ 105 169 cos 2 θ = 1 − 2 sin 2 θ = 1 − 2 ( 105 169 ) = 169 − 210 169 = − 41 169 tan 2 θ = sin 2 θ cos 2 θ = 16 √ 105 169 − 41 169 = − 16 √ 105 41 |
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