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 December 11th, 2016, 07:32 PM #1 Newbie   Joined: Dec 2016 From: USA Posts: 11 Thanks: 0 Hard problem-Find the exact value (Sin7.5°cos7.5°)(sin7.5°+cos7.5°)(sin7.5°-cos7.5°)(tan7.5°)(cot7.5°)=
December 11th, 2016, 08:11 PM   #2
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 Originally Posted by Kingsiso (Sin7.5°cos7.5°)(sin7.5°+cos7.5°)(sin7.5°-cos7.5°)(tan7.5°)(cot7.5°)=
Multiply the two middle factors; tan and cot are reciprocals ... their product is 1

$(\sin{7.5}\cos{7.5})(\sin^2{7.5}-\cos^2{7.5})(1)$

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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