Precalculus with Trigonometry
posted by Natalie .
Prove or disprove the following Identities:
cos(x)  sin(x) = cos(x) + sin (x)
sin raised to the 4 (theta)  cos raised to the 4 (theta) = sin squared (theta)  cos squared (theta)
cos (x+(pi)/(6)) + sin (x  (pi)/(3)) = 0
cos(x+y)cos(xy) = cos squared (x)  sin squared (y)
Sorry if you don't understand anything

Precalculus with Trigonometry 
MathGuru
For the first problem:
cos(x)  sin(x) = cos(x) + sin(x)
A few identities for negatives:
cos(x) = cos(x)
sin(x) = sin(x)
Therefore:
cos(x)  [sin(x)] = cos(x) + sin(x)
==================================
For your last problem:
cos(x+y)cos(xy) = cos^2(x)  sin^2(y)
Some identities:
cos(x+y) = cos(x)cos(y)  sin(x)sin(y)
cos(xy) = cos(x)cos(y) + sin(x)sin(y)
Multiplying using both identities:
[cos^2(x) cos^2(y)]  [sin^2(x) sin^2(y)]
Next, use the identity:
sin^2(x) + cos^2(x) = 1
[1sin^2(x)][1sin^2(y)]  [sin^2(x) sin^2(y)]
Multiply [1sin^2(x)][1sin^2(y)]:
1  sin^2(y)  sin^2(x) + [sin^2(x) sin^2(y)]  [sin^2(x) sin^2(y)]
We are left with this:
1  sin^2(y)  sin^2(x)
Which equals this:
cos^2(x)  sin^2(y)
===================
I'll stop there. I hope this helps.
Respond to this Question
Similar Questions

algebra
Can someone please help me do this problem? 
Mathematics  Trigonometric Identities
Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) = (sin^2y … 
Calculus
I wanted to confirm that I solved these problems correctly (we had to convert the polar curves to Cartesian equations). 1.rcos(theta)=1 x=1 2.r=2*sin(theta)+2*cos(theta) r^2=2rsin(theta)+2rcos(theta) x^2+y^2=2y+2x (a little unsure … 
trigonometry
can you correct the rest for me please? Express each as a function of theta: a. sin (270deg + theta)= cos theta b. cos (pi + theta)= cos theta c. tan (810 + theta)= ? 
trigonometry
can you correct the rest for me please? Express each as a function of theta: a. sin (270deg + theta)= cos theta b. cos (pi + theta)= cos theta c. tan (810 + theta)= ? 
Algebra II
Multiple Choice Which expression is NOT equivalent to 1? 
Precalculus 2
Similiarly to a question I asked previously I took the same approach. the problem is: what value(s) of theta solve the following equation? 
math(Trigonometry)
sin 2 theta + cos theta = 0 so, we use sin 2 theta = 2 sin theta cos theta right? 
Trigonometry
Prove the following identities: 1. (tan theta  sin theta)^2 + (1cos theta)^2 = (1sec theta) ^2 2. (12cos^2 theta) / sin theta cos theta = tan theta  cot theta 3. (sin theta + cos theta ) ^2 + (sin theta  cos theta ) ^2 = 2 Thank … 
Trigonometry
Prove the following identities: 1. (tan theta  sin theta)^2 + (1cos theta)^2 = (1sec theta) ^2 2. (12cos^2 theta) / sin theta cos theta = tan theta  cot theta 3. (sin theta + cos theta ) ^2 + (sin theta  cos theta ) ^2 = 2 Thank …