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December 11th, 2016, 08:32 PM   #1
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Hard problem-Find the exact value

(Sin7.5°cos7.5°)(sin7.5°+cos7.5°)(sin7.5°-cos7.5°)(tan7.5°)(cot7.5°)=
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December 11th, 2016, 09:11 PM   #2
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Quote:
Originally Posted by Kingsiso View Post
(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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