Prove this trigamtric equation.

Mathematics
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tan x + cot x = sec x csc x

Jun 23rd, 2015

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tan x + cot x = sec x csc x

let us start with the left side.

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....

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Jun 23rd, 2015

tan x + cot x = sec x csc x

let us start with the left side.

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

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