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Prove that: i) sin40^(@)cos50^(@)+cos4...

Prove that:
i) `sin40^(@)cos50^(@)+cos40^(@)sin50^(@)=1`
ii) `cot(270^(@)-theta)cot(270^(@)+theta)(cot(540^(@)-theta)cot(540^(@)+theta)=1`
iii) `cos(pi/8)+cos((3pi)/8)+cos((5pi)/8)+cos((7pi)/8)=0`

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Prove that: i) sin40^(@)cos50^(@)+cos40^(@)sin50^(@)=1 ii) cot(270^(@)-theta)cot(270^(@)+theta)(cot(540^(@)-theta)cot(540^(@)+theta)=1 iii) cospi/8+cos(3pi)/8+cos(5pi)/8+cos(7pi)/8=0

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Prove that cos theta + "sin " (270^(@) +theta) - "sin "(270^(@) -theta) + "cos " (180^(@) +theta) =0

Prove that: sin((3pi)/(8)-5)cos((pi)/(8)+5)+cos((3pi)/(8)-5)sin((pi)/(8)+7)=1

(sin theta)/(1-cos theta)=cos ec theta+cot theta

(1+cos.(pi)/(8))(1+cos.(3pi)/(8))(1+cos.(5pi)/(8))(1+cos.(7pi)/(8)) is equal to