Question

If cosA + sinA = √2 sin(90-A), then find the value of 1/(√2 + 1) cotA

Solve this

Answer 1

Hi ,

Given

cosA + sinA = √2 sin(90-A)

cosA + sinA = √2 cosA ----( 1 )

[ since sin(90-A ) = cosA ]

divide each term with sinA

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

cotA + 1 = √2 cotA

1 = √2 cotA - cotA

1 = (√2 - 1 )cotA

1 = { [ (√2 - 1 )(√2 + 1 ) ]/(√2 + 1 ) } cotA

1 = { [ (√2 )² - 1² ] /(√2 + 1 ) } cotA

1 = { (2 - 1 )/(√2 + 1 ) } cotA

1 = [ 1 / (√2 + 1 ) ] cotA

therefore ,

1 / ( √2 + 1 ) cotA = 1

I hope this helps you.

:)

Answer 2

cos A + sin A= √2 sin(90°-A)

» sin A + cos A = √2 cos A {sin(90-∅) = cos ∅}

» sin A = √2 cos A - cos A

Now,divide all terms by sin A
» sin A/sin A = √2cos A/sin A - cos A/sin A

» 1 = √2cot A - cot A {cos A/sin A = cot A}

» 1 = (√2-1) cot A

» Multiply and divide √2+1 on RHS,

» 1 = {(√2-1)(√2+1)/(√2+1)} × cot A

» 1 = (√2²-1²)/(√2+1) × cot A

» 1 = {1/(√2+1)} × cot A

Therefore! The value of 1/(√2+1) × cot A = 1

Hope it helps…