Question

If 8 tan x = 15, then find the value of sin x - cos x.
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Answer 1

Answer:

Step-by-step explanation:

tan x=15/8

therefore according to Pythagorean triplet

sin x=15/17

cos x=8/17

sin x-cos x= 15/17 - 8/17 = 7/17

Answer 2

Answer:

$8 \: tan \: x \: = 15$

$= tan \: x \: = \frac{15}{8}$

$as \: tan \: = \frac{p}{b}$

Let P = 15x

Let B = 8x

By Pythagoras Theorem,

${h}^{2} = {p}^{2} + {b}^{2}$

(H)² = (15x)² + (8x)²

(H)² = 225x² + 64x²

(H)² = 289x²

H = 17x

$sin \: x \: = \frac{p}{h}$

$six \: x = \frac{15x}{17x}$

cancelling x from x. we get,

$sin \: x = \frac{15}{17}$

Now,

$cos \: x \: = \frac{b}{h}$

$cos \: x \: = \frac{8x}{17x}$

cancelling x from x. we get,

$cos \: x \: = \frac{8}{17}$

Now,

$sin \: x \: - cos \: x \:$

Putting values of sin x and cos x

$\frac{15}{17} - \frac{8}{17}$

$= \frac{7}{17}$

Therefore,

$\frac{7}{17}$

is the answer.