Question

If sin theta + cos theta is equal to root 3 then prove that tan theta + cot theta is equal to 1

Answer 1

Step-by-step explanation:

Sinθ + Cosθ = √ 3

Squaring both the sides,

=> (Sinθ + Cosθ)^2 = (√ 3)^2

=> (Sinθ)^2 + (Cosθ)^2 + 2SinθCosθ = 3

=> Sin^2θ + Cos^2θ + 2sinθcosθ = 3

=> 1 + 2SinθCosθ = 3

=> 2SinθCosθ = 2

=> SinθCosθ = 1 ......(i)

Now,

tanθ + cotθ

= Sinθ/Cosθ + Cosθ/Sinθ

= Sin^2θ + Cos^2θ/SinθCosθ

= 1/SinθCosθ

= 1/1 (from(i))

= 1

Hence, proved....

Answer 2

Answer:

Please see the attachment