Question

if sin theta + cos theta is equals to root 3 then prove that 10 theta + cot theta is equal to 1
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Answer 1

Correct Question

If sin∅ + cos∅ = √3,then find prove that tan∅ + cot∅ = 1

Solution

Given that,

sin∅ + cos∅ = √3................[1]

To prove : tan∅ + cot∅ = 1

Squaring equation [1] on both sides,we get :

(sin∅ + cos∅)² = 3

→ sin²∅ + cos²∅ + 2sin∅cos∅ = 3

Since, sin²∅ + cos²∅ = 1

→2sin∅cos∅ = 2

→ sin∅cos∅ = 1..............[2]

Consider tan∅ + cot∅,

→ sin∅/cos∅ + cos∅/sin∅

→ (sin²∅ + cos²∅)/sin∅cos∅

→ 1/sin∅cos∅

→ 1 → RHS

Hence,Proved

Answer 2

Answer:

Step-by-step explanation:

Given :-

sin θ + cos θ = √3

To Prove :-

squaring on both sides,

Solution :-

sin θ + cos θ = √3

Squaring both sides, we get

⇒ (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)

⇒  L.H.S. = tan θ + cot θ

= Sin θ/cos θ  + cos θ/sin θ

= Sin² θ  + Cos² θ/Sin θ  × Cos θ  

= 1/1     [From Eq (i)]

R.H.S = 1

L.H.S = R.H.S

Hence Proved