Question

if sinx + cosx = √2 cos(90-x). Determine cotx.

Answer 1

sinx + cosx = √2 cos(90 - x)

sinx + cosx = √2 × cos(90 -x )

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We know, cos( 90 - Ф)= sinФ
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Then,

sinx + cosx =  √2 × sinx 

$\frac{sinx + cosx}{sinx} = \sqrt{2}$

$\frac{sinx}{sinx} + \frac{cosx}{sinx} = \sqrt{2}$

$1 + \frac{cosx}{sinx} = \sqrt{2}$

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We know, cosФ/sinФ = cotФ
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then,

$1 + \frac{cosx}{sinx} = \sqrt{2}$

1  + cotx =√2 

cotx = √2 - 1 



i hope this will help you



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