About Steve Holleran Expertise I can help with all math questions from basic math to Calculus.
Whether it`s consumer questions, or questions from high school or college students, I have probably dealt with it at some time in my career.
Experience 33 years teaching experience in NJ public schools
Education/Credentials B.S. Mathematics : Wake Forest University 1972
M.S. Mathematics : Monmouth University 1981
Question how would you solve these two identities step by step?
1. (sec X/ sin X)-(sin X/ cos X)=cot X
2. (sin X + cos X)^2= 1+ sin2x
Answer Hello Michael,
1. Working on the left side of this one, first let's get a common denominator: sin x * cos x. Then, combining the two fractions into one large fraction over the common denominator, we get:
[cos x * sec x - sin x * sin x] / [sin x * cos x]
= [cos x * 1/cos x - sin^2 x] / [ sin x * cos x]
= [1 - sin^2 x ] / [sin x * cos x]
= [ cos^2 x ] / [sin x * cos x] (using an identity
for 1-sin^2 x)
= cos x / sin x (cancelling out a factor of cos x)
= cot x
2. On this one, you want to square out the left hand side:
(sin x + cos x)^2 = sin^2 x + 2 sin x * cos x + cos^2 x
Now group the sin^2 x + cos ^2 x together and by identity, this equals 1. so now you have:
1 + 2 sin x * cos x
and the term 2 sinx * cos x is the identity for sin (2x),
