Question

Verify the trigonometric identity. cot(x)sec^4(x)=cot(x)+2tan(x)+tan^3(x)

Answer 1

sec^4 x = sec^2 x * sec^ 2 x = (sec^2 x)^2

Answer 2

cot(x)sec^4(x)
= cot(x)(sec^2(x))^2

Answer 3

then use the identity :
sec^2(x) = tan^2(x) + 1
therefore, the equation above can be
cot(x)(sec^2(x))^2
= cot(x)(tan^2(x) + 1)^2
expand the term in paranthesis to get
= cot(x) (tan^4(x) + 2 tan^2(x) + 1)
simplify again :
= cot(x) tan^4(x) + 2cot(x)tan^2(x) + cot(x)
=tan^4(x)/tan(x) + 2tan^2(x)/tan(x) + cot(x)
= tan^3(x) + 2tan(x) + cot(x)

proof

Answer 4

why when you simplify again so you get the cot and such

Answer 5

@primeralph

Answer 6

Hello?

Answer 7

i got it :) never mind but thankyou @primeralph

Answer 8

Okay, you're welcome.