Question

Solve the following equations :
(i) sin a + cos a= √2​

Answer 1

Step-by-step explanation:

divide both side by √(coeff of sin^2+cos^2)

use sin45=1/√2 and so on with cos

use sin(a+b)

Answer 2

Answer:

a =45°

Step-by-step explanation:

$\sin(a) + \cos(a) = \sqrt{2}$

Now, squaring both the sides...

${ \sin(a) }^{2} + { \cos(a) }^{2} + 2 \sin(a) \cos(a) = { \sqrt{2} }^{2}$

$we \: know \\ { \sin(a) }^{2} + { \cos(a) }^{2} = 1$

So,

$1 + 2 \sin(a) \cos(a) = 2$

$2 \sin(a) \cos(a) = 2 - 1$

$2 \sin(a) \cos(a) = 1$

$we \: know \\ 2 \sin(a) \cos(a) = \sin(2a)$

$\sin(2a) = 1$

$but \: \\ \sin(90) = 1$

$so \\ 2a = 90$

$hence \\ a = 45$

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