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Juan Set 2 Paper 1 · Q20

Paper 1Logic & proofTrigonometry

Let 0<a<π20<a<\dfrac{\pi}{2} satisfy

cos⁡2a−cos⁡(2a)=sin⁡(2a).\cos^2a-\cos(2a)=\sin(2a).

Which of the following is true for this value of aa?

Atan⁡a=15\tan a=\dfrac{1}{5}
Bcot⁡a=25\cot a=\dfrac{2}{\sqrt{5}}
Ccos⁡a=15\cos a=\dfrac{1}{\sqrt{5}}
Dcosec⁡a=5\operatorname{cosec}a=\sqrt{5}
Esin⁡(2a)=35\sin(2a)=\dfrac{3}{5}

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