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Answer 1

Theta is written as A.

Answer:

Required value of 5sinA - 12cosA is 0.

Step-by-step explanation:

Given,

tanA = $\dfrac{12}{5}$

From the properties of trigonometric functions :

• tanA = sinA / cosA

Here,

= > sinA / cosA = 12 / 5

= > 5 sinA = 12 cosA

= > 5sinA - 12cosA = 0

Hence the required value of 5sinA - 12cosA is 0.

Answer 2

Question :--

• if tan@ = 12/5, Find 5sin@ - 12cos@ = ?

Formula used :--

→ TanA = Perpendicular /Base = P/B

→ SinA = Perpendicular / Hypotenuse = P/H

→ CosA = Base / Hypotenuse = B/H .

→ Pythagoras theoram , P² + B² = H² .

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Solution :---

Given , Tan@ = 12/5

→ Tan@ = 12/5 = P/B

we get,

→ P = 12

→ B = 5

Now, putting value in Pythagoras theoram, we get,

→ (12)² + (5)² = H²

→ 144 + 25 = H²

→ 169 = H²

Square root both both sides we get,

→ H = 13 .

Putting this value now , we get,

→ sin@ = P/H = 12/13 .

→ cos@ = B/H = 5/13 .

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Now, putting these values in Question we get,

→ 5*(12/13) - 12*(5/13)

→ 60/13 - 60/13

→ 0

Hence, value of 5sin@ - 12cos@ is 0...