Question

if sin a + cos A = √2 sin (90 - A), then obtain the value of cot a​

Answer 1

Answer:

Given

sinA+cosA=

2

sin(90−A)

⇒

2

1

sinA+

2

1

cosA=sin(90−A)

⇒sinA.cos45

∘

+cosA+sin45

∘

=sin(90−A)

⇒(A+45

∘

)=sin(90

∘

−A)

Equating

A+45=90−A

⇒2A=45

∘

⇒A=22

2

1

∘

A=

8

π

∴cotA=cot

8

π

=

2

+1

Step-by-step explanation:

hope this will help you

Answer 2

Answer:

cot a = $\frac{1}{\sqrt{2}-1}$

Step-by-step explanation:

sin a +cos a = $\sqrt{2}$ sin(90- a)

=>sin a + cos a = $\sqrt{2}$ cos a

=>sin a = $\sqrt{2}$ cos a- cos a

=>sin a = cos a ($\sqrt{2} -1$)

=>$\frac{sin a}{cos a}$ = $\sqrt{2} -1$

=>$\frac{1}{cot a} = \sqrt{2}-1$

=>cot a = $\frac{1}{\sqrt{2}-1}$