Question

If sin 0 + cos 0 =3, then prove that tan 0+ cot=1​

Answer 1

Answer:

Step-by-step explanation:

(Sin 0 + Cos 0)² = 3²

Sin²0 + Cos²0 + 2Sin0Cos0 = 9

But,

{Sin²0+Cos²0=1}

So,

1+2Sin0Cos0 = 9

2Sin0Cos0 = 8

Sin0Cos0 = 8/2 = 4

To Prove :-

Tan0 + Cot0 = 1

Substituting values

Step-by-step explanation:

Step-by-step explanation:(Sin0 + Cos0)^2 = 3^2

Step-by-step explanation:(Sin0 + Cos0)^2 = 3^2Sin^2-0 + Cos^2-0 + 2sin0cos0 = 9

Step-by-step explanation:(Sin0 + Cos0)^2 = 3^2Sin^2-0 + Cos^2-0 + 2sin0cos0 = 92sin0cos0 = 3-1 = 2

Step-by-step explanation:(Sin0 + Cos0)^2 = 3^2Sin^2-0 + Cos^2-0 + 2sin0cos0 = 92sin0cos0 = 3-1 = 2Sin0cos0 = 2/2 = 1

Step-by-step explanation:(Sin0 + Cos0)^2 = 3^2Sin^2-0 + Cos^2-0 + 2sin0cos0 = 92sin0cos0 = 3-1 = 2Sin0cos0 = 2/2 = 1NOW,

Step-by-step explanation:(Sin0 + Cos0)^2 = 3^2Sin^2-0 + Cos^2-0 + 2sin0cos0 = 92sin0cos0 = 3-1 = 2Sin0cos0 = 2/2 = 1NOW,tan0 + cot 0

Step-by-step explanation:(Sin0 + Cos0)^2 = 3^2Sin^2-0 + Cos^2-0 + 2sin0cos0 = 92sin0cos0 = 3-1 = 2Sin0cos0 = 2/2 = 1NOW,tan0 + cot 0= Sin0/cos0 + cos0/sin0

Step-by-step explanation:(Sin0 + Cos0)^2 = 3^2Sin^2-0 + Cos^2-0 + 2sin0cos0 = 92sin0cos0 = 3-1 = 2Sin0cos0 = 2/2 = 1NOW,tan0 + cot 0= Sin0/cos0 + cos0/sin0= Sin^2-0 + cos^2-0/ sin0cos0

Step-by-step explanation:(Sin0 + Cos0)^2 = 3^2Sin^2-0 + Cos^2-0 + 2sin0cos0 = 92sin0cos0 = 3-1 = 2Sin0cos0 = 2/2 = 1NOW,tan0 + cot 0= Sin0/cos0 + cos0/sin0= Sin^2-0 + cos^2-0/ sin0cos0= 1/1 = 1.