Question

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

Solve this

Answer 1

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…

Answer 2

given ,
cos A+ sin A= √2sin (90-A)
=√2cosA.[ {sin(90-A)}=cosA]
sinA= √2cosA- cos A
dividing BOTH side by sinA
1= √2cosA/sinA- cos/sinA
1= √2cot A - cotA
1= cot A( √2-1)
multiplying RHS side by (√2+1) & dividing by (√2+1)
1= cot A (√2-1)(√2+1)/(√2+1)
1= cot A (2-1)(√2+1)
1= cot A(√2+1)
1/[cotA(√2+1)]= 1

therefore ur answer is 1.