Question

if sinA + cosA =√2 cos (90-A), find cotA​

Answer 1

Answer:

SinA + cosA=√2sin(90-A)

or, sinA + cosA= √2cosA {as sin(90-¢)=cos¢}

or, sinA÷cosA + 1= √2 {divided by cosA}

or, tanA = (√2-1)

or, cotA= 1÷(√2-1) {as cotA= 1/ tanA}

or, cotA= (√2+1)÷{(√2+1)×(√2-1)}

or, cotA= (√2+1)÷(2-1)

or, cotA=(√2+1)

{using a^2 - b^2=(a+b)(a-b)}

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Answer 2

Answer:

cot A=√2-1

Step-by-step explanation:

sinA+ cosA = √2 cos (90-A)

sinA+cosA=√2sinA

cosA=√2 sinA - sinA

cosA= sinA (√2-1) (Taking common)

cosA÷ sinA = √2-1

cotA=√2-1

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