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Question

How do you solve sinx+cosx=1?


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Solution

Find the general solution of given trigonometric equation

Given: sinx+cosx=1

Squaring on both sides we get,

sinx+cosx=1

12sinx+12cosx=12

sinπ4sinx+cosxcosπ4=12

cos(x-π4)=12

x-π4=2nπ±π4

x-π4=2nπ-π4x=2(taking+sign)

x-π4=2nπ+π4x=2+π2(taking-sign)

x=π2+2πn,2πn { n is any integer}

Hence the answer is x=π2+2πn,2πn { n is any integer}


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