Question

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Answer 1

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Answer 2

Answer:

First of all we have to find the measures missing sides,

so, let us find the length of side CB,

side CB is the hypotenuse as it is opposite of ∠BDC which is of 90°,

∴ by pythagoras theorem,

(CB)² = (CD)² + (BD)²

∴ (CB)² = (4)² + (3)²

∴ (CB)² = 16 + 9

∴ (CB)² = 25

∴ CB = √25

∴ CB = 5

Similarly, Side AB is the hypotenuse of the ΔABC,

∴ (AB)² = (AC)² + (BC)²

∴ (AB)² = (12)² + (5)²

∴ (AB)² = 144 + 25

∴ (AB)² = 169

∴ AB = √169

∴ AB = 13

Now,

sinФ = Opposite side

             hypotenuse

∴ sin A = CB  = 5

               AB     13

Similarly,

cosФ = adjacent side  

              hypotenuse

∴ cos A = AC  = 12

                AB      13

Now,

your question is cosA - sinA,

∴ cosA -sinA = 12 - 5  = 12 - 5  =  7

                        13   13       13          13

∴ Your ans is d) 7

                         13

Step-by-step explanation: