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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