Question

if sina+cosa=√2sin(90°-a) then find the value of cosa

Answer 1

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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