prove trig identies work and steps?

Question

work and steps pleae
1. tan(pi/4-phata) = 1- tan phata / 1+ tan phata
2. cos(x+y)+ cos (x-y) = 2 cosxcosy

Answer 1

Where are you coming up with the word "phata"? No such word exists in the world of trigonometry. The word you are probably thinking of is the Greek letter "theta," which is represented by the symbol Θ, which you can produce by first pressing down the "alt" key and then the number 233 on the 10-key keyboard of your computer console. The "e" in the first syllable of the word theta is pronounced as a long "a", as in the word "fate," and the letters "th" have a hard pronunciation, as in the word "theater."

To find out how to produce all of the ASCII characters, visit this website:

http://asciitable.com/

Answer 2

1. tan(pi/4-phata) = 1- tan phata / 1+ tan phata
tan(pi/4-x)
= [tan(pi/4)-tan(x)]
/[1+tan(pi/4)tan(x)]
= [1-tan(x)]/[1+tan(x)], since tan(pi/4) = 1

2.cos(x+y)+ cos (x-y) = 2 cosxcosy
LHS
= cosxcosy-sinxsiny + cosxcosy - sinxsiny
= 2cosxcosy

Answer 3

1.)
tan((pi/4) - A) = (1 - tan(A))/(1 + tan(A))

tan((pi/4) - A) = (tan(pi/4) - tan(A))/(1 + tan(pi/4)tan(A))
tan((pi/4) - A) = (1 - tan(A))/(1 + tan(A))

tan(pi/4) = 1

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2.)
cos(x + y) + cos(x - y) = 2cos(x)cos(y)

cos(x + y) = cos(x)cos(y) - sin(x)sin(y)
cos(x - y) = cos(x)cos(y) + sin(x)sin(y)

cos(x + y) + cos(x - y) = cos(x)cos(y) - sin(x)sin(y) + cos(x)cos(y) + sin(x)sin(y)

cos(x + y) + cos(x - y) = cos(x)cos(y) + cos(x)cos(y)
cos(x + y) + cos(x - y) = 2cos(x)cos(y)