Question

Cos A = square root 21 divided by 5 and sin A = 2/5. What is the exact value of cos 2A?

Answer 1

`cos\alpha=(√(21))/(5);\ sin\alpha=(2)/(5)\\\\\\cos2\alpha=cos^2\alpha-sin^2\alpha\\\\cos^2\alpha=\left((√(21))/(5)\right)^2=(21)/(25)\\\\sin^2\alpha=\left((2)/(5)\right)^2=(4)/(25)\\\\cos2\alpha=(21)/(25)-(4)/(25)=(17)/(25)`