Question

If sin0+ cos0=√2 sin(90-0), determine cot0

Answer 1

Theta ( $\theta$ ) is written as A.

Answer:

Required value of cotA is √2 + 1 .

Step-by-step explanation:

Here,

sinA + cosA = √2 sin( 90 - A )

From the properties of trigonometry :

• sin( 90 - B ) = cos B , where B is an angle.

Therefore, here, in the same way, sin( 90 - A ) = cos A

Now,

= > sinA + cosA = √2 cosA

= > ( sinA + cosA ) / cosA = √2

= > ( sinA / cosA ) + ( cosA / cosA ) = √2

= > tanA + 1 = √2 { sinB / cosB = tanB }

= > tanA = √2 - 1

= > 1 / ( √2 - 1 ) = 1 / tanA

Multiplying & dividing left hand side by √2 + 1 :

= > 1 / ( √2 - 1 ) x ( √2 + 1 ) / ( √2 + 1 ) = cotA { where A ≠ nπ , n € whole numbers }

= > ( √2 + 1 ) / { ( √2 )^2 - 1^2 } = cotA { using ( a + b )( a - b ) = a^2 - b^2 , ( √2 + 1 )( √2 - 1 ) = ( √2 )^2 - ( 1 )^2 }

= > ( √2 + 1 ) / ( 2 - 1 ) = cotA

= > ( √2 + 1 ) / 1 = cotA

= > √2 + 1 = cotA

Hence the required value of cotA is √2 + 1 .