Proving Other Trigonometric Identities

Question

Prove that:

 

1 + cos x =     sin x   

    sin x        1 - cos x

Answer 1

Muslim,

 

This is the Pythagoreanidentity of trigonometry which can be shown first by multiplying out the fractions:

1-cos²x=sin²x 

 

Say you have triangle with adjacent side a,opposite side b, and hypotenuse c of an angle. Then cos of that angle is a/c, sin is b/c plug bepause ofPythagoras we know a²+b²=c² .

 

If we plug in cos and sin into the original equation we get

1-a2/c2=b2/c²

Multiply through with c²

Now c²-b²=a²

And c²=a²+b²=c² //