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tanx = 5/2

from trigonometry, tanx = opp/adj

opp = 5

adj = 2

Also, from pythagoras theorem, hyp^{2} = opp^{2} + adj^{2}

hyp^{2} = 5^{2} + 2^{2}

hyp^{2} = 25 + 4

take the square root of both sides,

hyp = √29

sinx = opp/hyp = 5/√29

cosx = adj/hyp = 2/√29

Therefore, sinx + cosx = 5/√29 + 2/√29

= (5+2)/√29

= 7/√29

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