Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

    
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,428 questions

17,804 answers

1,438 comments

47,178 users

trigonometry!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

+1 vote
Verify tan x +2 cot x =sec x csc x+cot x
asked Feb 14, 2013 in TRIGONOMETRY by anonymous Apprentice

2 Answers

+1 vote

LHS tan(x) + 2cot(x)

tan(x) + cot(x) + cot(x)

Quotient Identities: tan(θ) = sin(θ)/cos(θ) and cot(θ) = cos(θ)/sin(θ)

[sin(x)/cos(x) + cos(x)/sin(x)] + cot(x)

Rewrite the expression with common denominator.

[sin2(x) + cos2(x)]/[sin(x)cos(x)] + cot(x)

Pythagorean Identities: sin2(θ) + cos2(θ) = 1

1/[sin(x)cos(x)] + cot(x)

[1/sin(x)]*[1/cos(x)] + cot(x)

Reciprocal identities: 1/isn(θ)=coses(θ) and 1/cos(θ)=sec(θ).

coses(x)sec(x) + cot(x) RHS

Therefore tan(x) + 2cot(x) = sec(x)coses(x) + cot(x).

answered Feb 14, 2013 by richardson Scholar
0 votes

The trigonometric equation is tan x + 2 cot x = sec x csc x + cot x.

Right hand side identity = sec x csc x + cot x.

Using reciprocal identities : sec x = 1/cos x and csc x = 1/sin x.

sec x csc x + cot x = (1/cos x)(1/sin x) + cot x

= (1/cos x sin x) + cot x

Pythagorean Identities: sin2(x) + cos2(x) = 1.

= (sin2x + cos2x)/(cos x sin x) + cot x

= (sin2x/cos x sin x) + (cos2x/cos x sin x) + cot x

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

Trigonometry identities : tan x = sin x/cos x and cot x = cos x/sin x.

= tan x + cot x + cot x

= tan x + 2 cot x

= Left hand side identity.

answered Jul 8, 2014 by lilly Expert

Related questions

asked Dec 22, 2014 in TRIGONOMETRY by anonymous
asked Jul 24, 2014 in TRIGONOMETRY by anonymous
asked Jul 11, 2014 in TRIGONOMETRY by anonymous
asked May 18, 2014 in TRIGONOMETRY by anonymous
asked May 13, 2014 in TRIGONOMETRY by anonymous
...