Question

If tan+cot=2 then sin+cos=?

Answer 1

Answer:

tanθ+cotθ=2

sinθ/cosθ+cosθ/sinθ =2

sin²θ+cos²θ/cosθsinθ =2

1/cosθsinθ =2

cosθsinθ=1/2

(sinθ+cosθ)²=sin²θ +cos²θ +2sinθcosθ

(sinθ+cosθ)²=1+2*1/2

(sinθ+cosθ)²=1+1=2

sinθ+cosθ=√2

Step-by-step explanation:

Answer 2

Answer:

√2

Step-by-step explanation:

we have,

tanx+cotx = 2

sinx/cosx+cosx/sinx = 2

(sin²x+cos²x)/sinxcosx = 2

1/sinxcosx = 2

1 = 2sinxcosx

so, 1 = sin2x

as we know,,

sin²x+cos²x = 1

can also be written as,

(sinx+cosx)²-sin2x = 1

(sinx+cosx)²-1 = 1

(sinx+cosx)² = 2

so, sinx+cosx = √2 ....ans.