SOLUTION: Will you please help me with this equation: Given: sin (x+y)=sin x cos y + cos x sin y and cos (x+y) = cos x cos y - sin x sin y. Simplify ; sin ( x + pi ) × tan (x +pi/2) × sec
Algebra.Com
Question 1010663: Will you please help me with this equation: Given: sin (x+y)=sin x cos y + cos x sin y and cos (x+y) = cos x cos y - sin x sin y. Simplify ; sin ( x + pi ) × tan (x +pi/2) × sec (pi/2 - x)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's break the problem into smaller pieces
-----------------------------------------------------
Use the given identity
Use the unit circle
Multiply
Simplify. We'll call this Equation A
-----------------------------------------------------
Use the given identity
Use the unit circle
Multiply
Simplify. We'll call this Equation B
-----------------------------------------------------
Use the given identity
Use the unit circle
Multiply
Simplify. We'll call this Equation C
-----------------------------------------------------
Use the given identity
Use the unit circle
Multiply
Simplify. We'll call this Equation D
-----------------------------------------------------
Use the identity sec = 1/cos.
Substitute (see Equation D). We'll call this Equation E
-----------------------------------------------------
Use the identity tan = sin/cos
Perform a substitution (see equation B)
Perform a substitution (see equation C)
Simplify. We'll call this Equation F
-----------------------------------------------------------------------------
-----------------------------------------------------------------------------
-----------------------------------------------------------------------------
-----------------------------------------------------------------------------
Now onto the main problem
Original Given Problem
Apply a substitution (see equation A)
Apply a substitution (see equation F)
Apply a substitution (see equation E)
-----------------------------------------------------
So, simplifies to
RELATED QUESTIONS
Can you help me please ;Given; sin (x+y) = sin x cos y + cos x sin y and cos (× + y)= (answered by Boreal,solver91311)
Can you help me please; Given sin (x+y) = sin x cos y + cos x sin y and cos (x+y) =... (answered by Alan3354)
Can you help battle with this; Given ; sin(x+y) = sin x cos y +cos x sin y and cos... (answered by Alan3354)
Simplify cos(x)cos(y) +... (answered by Edwin McCravy)
Verify the identity.
(cos(x) - cos(y))/(sin(x) + sin(y)) + (sin(x) - sin(y))/(cos(x) + (answered by solver91311)
Simplify... (answered by addingup)
Given sin (x+y)= sin x cos y + cos x sin y
and cos(x+y) = cos x cos y -sin x sin y... (answered by Alan3354)
sin(x+y)=sin(x)cos(y)+sin(y)cos(x)
20 sin(x)+21... (answered by Edwin McCravy)
Given sin (x+y)= sin x cos y + cos x sin y
and cos(x+y) = cos x cos y - sin x sin y... (answered by Alan3354)