Q. 324.5( 51 Votes )

If sin θ + cos θ

Answer :

Given - sin θ + cos θ = √3


To Prove - tan θ + cot θ =1


Property - sin2 θ + cos2 θ = 1


Answer Given equation –


sin θ + cos θ = √3


squaring on both sides,


(sin θ + cos θ)2 = 3


sin2 θ + cos2 θ + 2sin θ. cos θ = 3


1 + 2sin θ. cos θ = 3 ………( sin2 θ + cos2 θ = 1)


2sin θ. cos θ = 2


sin θ. cos θ = 1 ………(1)


Now,


L.H.S. = tan θ + cot θ




………from (1)


= 1


= R.H.S.


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


Hence Proved !!!


OR


Properties –


1. cos θ = sin (90 – θ)


2. tan θ = cot (90 – θ)


3. sin2 θ + cos2 θ = 1


4. tan θ. cot θ = 1


Answer –




………by properties given above




………by properties given above


= 1 + 2


= 3


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