Prove this trigamtric equation.

Mathematics
Tutor: None Selected Time limit: 1 Day

tan x + cot x = sec x csc x

Jun 23rd, 2015

Thank you for the opportunity to help you with your question!

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....

please wait as I continue with your answer. Thanks

Please let me know if you need any clarification. I'm always happy to answer your questions.
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

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Jun 23rd, 2015
...
Jun 23rd, 2015
May 30th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer