Question

if 8 tan 0=15, then sinx-cos x is equal to
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Answer 1

Answer:

sinx - cos x =1

Step-by-step explanation:

∵ 8 tan X =15

∴ tan X = $\frac{15}{8}$

∵ tan X = $\frac{opposite}{adjacent}$

∴ opposite = 15 , adjacent = 8

∵ hypotenuse² =   opposite²  + adjacent²

∴ hypotenuse = $\sqrt{15^{2} +8^{2} }$ = 7

∴ opposite = 15 , adjacent = 8 , hypotenuse = 7

∵ sin X = $\frac{opposite}{hypotenuse}$

∴ sin X = $\frac{15}{7}$    ---------> (1)

∵ cos  X = $\frac{adjacent}{hypotenuse}$

∴ cos X = $\frac{8}{7}$    ---------> (2)

by subtracting (2) from (1) :

∴ sinx - cos x = $\frac{15}{7}$  -  $\frac{8}{7}$ = 1