Question

Sin a + cos a = √2 , (a =/= 90° ) then value of tan a is​

Answer 1

Answer:

I hope it will help you...

Answer 2

Answer:

Tan A = 1

Step-by-step explanation:

Given :

Sin A + Cos A = √2

To Find :

Tan A = ?

Solution :

We know that,

Sin² A + Cos² A = 1

So,

from given Equation,

Sin A + Cos A = √2

(Sin A + Cos A)² = (√2)² (squaring both the sides)

Sin² A + Cos² A + 2 Sin A Cos A = 2

(Sin² A + Cos² A) + 2 Sin A Cos A = 2

1 + 2 Sin A Cos A = 2

2 Sin A Cos A = 1

By multiplying by (-1) on both the sides,

- 2 Sin A Cos A = - 1

By adding 1 both the sides,

1 - 2 Sin A Cos A = 1 - 1 = 0

1 - 2 Sin A Cos A = 0

(Sin² A + Cos² A) - 2 Sin A Cos A = 0

(Sin A - Cos A)² = 0

Sin A - Cos A = 0

Sin A = Cos A

By divinding both the sides by Cos A,

$\frac{Sin \ A}{Cos \ A}=\frac{Cos \ A}{Cos \ A}$

⇒ Tan A = 1