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December 11th, 2016, 08:32 PM  #1 
Newbie Joined: Dec 2016 From: USA Posts: 11 Thanks: 0  Hard problemFind the exact value
(Sin7.5°cos7.5°)(sin7.5°+cos7.5°)(sin7.5°cos7.5°)(tan7.5°)(cot7.5°)=

December 11th, 2016, 09:11 PM  #2  
Math Team Joined: Jul 2011 From: Texas Posts: 2,656 Thanks: 1327  Quote:
$(\sin{7.5}\cos{7.5})(\sin^2{7.5}\cos^2{7.5})(1)$ Note $\cos^2{t}\sin^2{t}=\cos(2t)$ and $2\sin{t}\cos{t}=\sin(2t)$ ... $\left(\dfrac{1}{2} \cdot 2\sin{7.5}\cos{7.5}\right)(\cos{15})$ $\dfrac{1}{2}\sin{15}\cos{15}$ $\dfrac{1}{4} \cdot 2\sin{15}\cos{15}$ $\dfrac{1}{4} \sin{30} = \dfrac{1}{8}$  

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