##### Prove this trigamtric equation.

label Mathematics
account_circle Unassigned
schedule 1 Day
account_balance_wallet \$5

tan x + cot x = sec x csc x

Jun 23rd, 2015

tan x + cot x = sec x csc x

tan x + cot x = (cos x / sin x) + ( sin x / cos x)

the next step, get a common denominator

(cos x / sin x) + ( sin x / cos x) = (cos^2 x / sin x.cos x) + (sin^2 x / sin x . cos x)

combine the fractions into one....

Jun 23rd, 2015

tan x + cot x = sec x csc x

tan x + cot x = (cos x / sin x) + ( sin x / cos x)

the next step, get a common denominator

(cos x / sin x) + ( sin x / cos x) = (cos^2 x / sin x.cos x) + (sin^2 x / sin x . cos x)

combine the fractions into one

(cos^2 x / sin x.cos x) + (sin^2 / sin x.cos x) = (cos^2 x + sin^2 x) / (sin x.cos x)

simplify because the numerator reveals a Pythagorean identity

(cos^2 x + sin^2 x) / (sin x.cos x) = 1 / (sin x.cos x)

split the RHS to be

1 / (sin x.cos x) = (1/sin x) ( 1/cos x)

convert the fraction into their reciprocal form

Ans (1/sin x) ( 1/cos x) = (sec x) (csc x)

Jun 23rd, 2015

...
Jun 23rd, 2015
...
Jun 23rd, 2015
Sep 25th, 2017
check_circle