Question

Given that tan x=5/12, what is the value of sin+cosx?

Answer 1

let perpendicular be 5y

let base be 12 y

so ,

hypotenuse square is equal to 5y square plus 12y square so hypotenuse is 13y

sin x = 5/13

cos x = 12/13

adding both of them

sinx+cosx = 17/13

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Answer 2

Answer:

if tan x = 5/12

means perpendicular is 5x and base is 12x therefore hypotenuse = √ (5x)² + (12x)²

√ (25x² + 144x²)

=> √169x²

=> 13 x

Now sin x = perpendicular / hypotenuse

=> 5x/13x

=> 5/13

cos x = 12x/13x

=> 12/13

sin x + cos x = 5/13 + 12/13

=> 17/13