Question

If sin+cos=√2 then find tan+cot...?

Answer 1

Answer:

Step-by-step explanation:

Sin+cos=√2

Squaring on both sides,we get

Sin^2+cos^2+2 sin.cos=2

1+sin.cos=2

Sin.cos=1/2

We have to find tan+cot

Putting value of tan n cot

Sin/cos+cos/sin

Sin^2+cos^2/cos.sin

1/(1/2)

=2 is the answer

Hope you will get!!

Mark it as brainlist pls

Answer 2

Answer:

2

Step-by-step explanation:

tan +cot=

sin/cos + cos/sin

= sin^2 + cos^2 / sin*cos

= 1 / sin*cos

= cosec*sec                       [1]

(sin + cos )^2 = 2        [by squaring both the sides ]

sin^2 + cos^2 + 2sincos = 2

1 + 2sincos = 2

2sincos - 2 = -1

2 ( sin*cos - 1 )  = -1

sin*cos - 1 = -1/2

sin*cos = -1/2 + 1

sin*cos = 1/2

therefor....     1/cosec*sec = 1/2

cosec*sec= 2

since tan + cot = cosec*sec  ( from 1 . proved above )

tan + cot = 2