Question

if 8 tanx = 15, then sinx - COSX is equal to
17/5
7/17
1/17
8/17




ans plz ​

Answer 1

EXPLANATION.

⇒ 8tanx = 15.

As we know that,

⇒ tan(x) = 15/8.

tan∅ = perpendicular/base.

By using Pythagoras theorem, we get.

⇒ H² = P² + B².

⇒ H² = (15)² + (8)².

⇒ H² = 225 + 64.

⇒ H² = 289.

⇒ H = √289.

⇒ H = 17.

sin∅ = perpendicular/hypotenuse. = 15/17.

cos∅ = Base/hypotenuse. = 8/17.

tan∅ = perpendicular/base. = 15/8.

cosec∅ = hypotenuse/perpendicular = 17/15.

sec∅ = hypotenuse/base. = 17/8.

cot∅ = base/perpendicular. = 8/15.

To find value of,

(1) = sin(x) - cos(x).

⇒ 15/17 - 8/17.

⇒ 15 - 8/17.

⇒ 7/17.

option [B] is correct answer.

                                                                                                                     

MORE INFORMATION.

(1) = Relation between systems of measurement of angles.

D/90 = G/100 = 2C/π.

(2) = Fundamental trigonometric identities.

(a) = sin²∅ + cos²∅ = 1.

(b) = 1 + tan²∅ = sec²∅.

(c) = 1 + cot²∅ = cosec²∅.

Answer 2

Answer:

Given :-

• 8 tanx = 15

To Find :-

• What is the value of sinx - cosx.

Formula Used :-

$\sf\boxed{\bold{\small{sin\theta =\: \dfrac{Perpendicular}{Hypotenuse}}}}$

$\sf\boxed{\bold{\small{cos\theta =\: \dfrac{Base}{Hypotenuse}}}}$

$\sf\boxed{\bold{\small{{(Hypotenuse)}^{2} =\: {(Perpendicular)}^{2} + {(Base)}^{2}}}}$

Solution :-

Given :

$\mapsto$ 8 tanx = 15

Then,

↦ $\sf tanx =\: \dfrac{15}{8}$

As we know that,

✯ $\sf\boxed{\bold{\small{tan\theta =\: \dfrac{Perpendicular}{Base}}}}$ ✯

Then, from formula we can tell that,

• Perpendicular = 15
• Base = 8

According to the question by using the formula we get,

⇒ $\sf {(Hypotenuse)}^{2} =\: {(15)}^{2} + {(8)}^{2}$

⇒ $\sf {(Hypotenuse)}^{2} =\: 225 + 64$

⇒ $\sf {(Hypotenuse)}^{2} =\: 289$

⇒ $\sf Hypotenuse =\: \sqrt{289}$

➠ $\sf\bold{\pink{Hypotenuse =\: 17}}$

Now we get that,

• Perpendicular = 15
• Base = 8
• Hypotenuse = 17

Then,

➤ $\sf sin\theta =\: \dfrac{Perpendicular}{Hypotenuse} =\: \dfrac{15}{17}$

➤ $\sf cos\theta =\: \dfrac{Base}{Hypotenuse} =\: \dfrac{8}{17}$

Now we have to find the value of sinx - cosx,

Given :

• sinx = $\sf \dfrac{15}{17}$
• cosx = $\sf \dfrac{8}{17}$

Then,

⇒ $\sf sinx -\: cosx$

⇒ $\sf \dfrac{15}{17} -\: \dfrac{8}{17}$

⇒ $\sf \dfrac{15 - 8}{17}$

➠ $\sf\bold{\purple{\dfrac{7}{17}}}$

Hence, the correct options is option no 2) 7/17.

${\underline{\boxed{\small{\bf{\therefore The\: value\: of\: sinx\: -\: cosx\: is\: \dfrac{7}{17}.}}}}}$