Question

of tan theta =5/12 ,find the value of (costheta +sintheta)/(costheta-sintheta)​

Answer 1

Given:- $\red{\sin\theta =\dfrac{5}{12}}$

To Find :- $\red{\dfrac{\cos\theta+\sin\theta}{\cos\theta-\sin\theta}}$

Answer:- We have tanθ = 5/12 . We know tanθ = perpendicular/base . So ,

=> hypontenuse ² = base² + perpendicular ².

=> hypontenuse ² = 12² + 5².

=> hypontenuse ² = 144 + 25

=> hypontenuse ² = 169 .

=> hypontenuse = √169.

★ hypontenuse = 13 .

So ;

• sinθ = perp./hypo. = 5/13.
• cosθ = base/hypo. = 12/13 .

Hence ; cosθ + sinθ / cosθ - sinθ

= 12/13 + 5/13 ÷ 12/13 - 5/13

= 12 + 5/13 ÷ 12 - 5/13

= 17/13 ÷ 7/13

= 17/13 × 13/7

= 17/7 .

★ Hence the required answer is 17/7.