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

13,435 questions

17,804 answers

1,438 comments

97,177 users

Prove please :)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

0 votes

prove

sin^2y-sin^2x=1/(1+tan^2x)-1/(1+tan^2y)

asked Mar 25, 2013 in TRIGONOMETRY by M Gravity Rookie

1 Answer

+1 vote

Take R.H.S =1/(1+tan2x)-1/(1+tan2y)

Recall : Trigonometry formulas tan^2A = sin2A/cos2A

Substitute tan^2x = sin2x / cos2x in the R.H.S.

R.H.S =1/(1 + sin2x/cos2x) - 1(1+ sin2y / cos2y)

R.H.S =1/(cos2x +sin2x) / cos2x - 1/(cos2y + sin2y)/cos2y

Recall : Trigonometry forumalas sin2A +cos2A = 1

Substitute cos2x + sin2x = 1 and cos2y + sin2y = 1 in the R.H.S

R.H.S = 1/(1)/cos2x - 1/(1)/cos2y

R.H.S = cos2x - cos2y

Recall : Trigonometry formulas cos2A = 1 - sin2A

Substitute cos2x = 1 - sin2x and cos2y = 1 - sin2y

R.H.S = 1 - sin2x -(1 - sin2y)

Recall : Distributive property a(b - c) = ab - ac

R.H.S = 1 - sin2x -1 + sin2y

R.H.S = 0 + sin2y - sin2x

There fore R.H.S = sin2y - sin2x =  L.H.S

L.H.S. = R.H.S.

There fore sin^2y-sin^2x=1/(1+tan^2x)-1/(1+tan^2y)

 

answered Mar 27, 2013 by diane Scholar

Related questions

asked Oct 3, 2014 in CALCULUS by anonymous
asked Oct 3, 2014 in CALCULUS by anonymous
asked Oct 3, 2014 in CALCULUS by anonymous
asked Oct 2, 2014 in CALCULUS by anonymous
asked Oct 2, 2014 in CALCULUS by anonymous
asked Oct 2, 2014 in CALCULUS by anonymous
asked Oct 2, 2014 in CALCULUS by anonymous
asked Oct 2, 2014 in CALCULUS by anonymous
asked Oct 3, 2014 in CALCULUS by anonymous
asked Oct 3, 2014 in CALCULUS by anonymous
asked Nov 4, 2014 in TRIGONOMETRY by anonymous
asked Oct 27, 2019 in TRIGONOMETRY by anonymous
...