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Verify the identity.

 

cos(x)/1+sin(x)=sec(x)-tan(x)

 Jul 17, 2014

Best Answer 

 #2
avatar+130466 
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cos(x)/(1+sin(x)) =sec(x)-tan(x)

OK, on the right side we have

1/cos(x) - sin(x)/cos(x)

(1 - sin(x)) /  cos(x)    Multiply numerator and denominator by cos(x)

[(cos(x)* (1- sin(x)] / [cos2(x)]

[(cos(x)* (1- sin(x)]/ (1 - sin2(x))

[(cos(x)* (1- sin(x)]/ [(1 + sin(x)) * (1 - sin(x)]

cos(x)/(1+sin(x))   which equals the left hand side

 

 Jul 18, 2014
 #1
avatar+8262 
+5

I don't know what the identity is but the answer is tan_rad(((pi*x)/180))=-sin_rad(((pi*x)/180))sec(((pi*x)/180))-cos_rad(((pi*x)/180))

 Jul 17, 2014
 #2
avatar+130466 
+5
Best Answer

cos(x)/(1+sin(x)) =sec(x)-tan(x)

OK, on the right side we have

1/cos(x) - sin(x)/cos(x)

(1 - sin(x)) /  cos(x)    Multiply numerator and denominator by cos(x)

[(cos(x)* (1- sin(x)] / [cos2(x)]

[(cos(x)* (1- sin(x)]/ (1 - sin2(x))

[(cos(x)* (1- sin(x)]/ [(1 + sin(x)) * (1 - sin(x)]

cos(x)/(1+sin(x))   which equals the left hand side

 

CPhill Jul 18, 2014

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