Identities problems

[waunar]

I have tried to solve this problems several times but i am yet to get the concept. can you help me with this?

Simplify the expression

sin^3@ + cos^3@/sin@ + cos@ (note theta is represented with@).

another problem is vertifing the identity by transforming the left hand side into the right-hand side.

Cos^2@(sec^2 @-1)= sin^2 @

On this problem i am confused about the transformation process. any help will be appriciated.

 

[royhaas]

Use the following facts:

\(\displaystyle x^3+y^3 = (x+y)(x^2-xy+y^2)\)

and

\(\displaystyle tan^2(\theta)+1=sec^2(\theta)\).

 

[waunar]

Use the following facts:

\(\displaystyle x^3+y^3 = (x+y)(x^2-xy+y^2)\)

and

\(\displaystyle tan^2(\theta)+1=sec^2(\theta)\).

I understand tan^2@ + 1=sec^2@. but how do you transform the equation to equal sin^2@

 

[galactus]

I understand tan^2@ + 1=sec^2@. but how do you transform the equation to equal sin^2@

Just remember the fact that \(\displaystyle \frac{sin{\theta}}{cos{\theta}}=tan{\theta}\)