Prove: (tan y + Cot y) sin y cos y = 1

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To prove the equation (tan y + cot y) sin y cos y = 1, the discussion highlights the initial steps taken, including substituting cotangent with its reciprocal and finding a common denominator. The user simplifies the expression to cos y sin y tan y + cos² y but struggles to show it equals 1. A suggestion is made to express tangent and cotangent in terms of sine and cosine fractions for simplification. Ultimately, the user successfully finds the solution after applying these suggestions.
Jasonp914
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Hi, I need to prove:

(tan y + Cot y) sin y cos y = 1

I've gotten this far and got stuck:

(tany + cos y) sin y cos y changed Cot to reciprical
--------sin y

(sin y tany + cosy) sin y cos y common demonator
--------siny

(sin y tany + cos y) cosy multipyied by sin y

then i could distribute

cos y sin y tan y + cos(sqared) y but how would that equal 1?

thanks for your time.
 
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It should help if you plug in

\tan x = \frac{\sin x}{\cos x}[/itex]
 
Last edited:
just a suggestion of my own, but try expressing those ratios literally in terms of fractions (ie: sin theta = o/h)...simplify the equation now and see if you notice anything familiar.
 
o got it thank you!
 

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