Question

......hey ans me this one.....​

Answer 1

What is trigonometry ?

 Trigonometry is the study of angles and the ratios of sine, cosine, tangent, cosec, sectant and cot. It includes a number of trigonometric identity laws and some relation between ratios.

Some of the laws are :

• sinθ * cosecθ = 1

• cosθ * secθ = 1

• tanθ * cotθ = 1

• sin(90° - θ) = cosθ and vice versa

• tan(90° - θ) = cotθ and vice versa

• sec(90° - θ) = cosecθ and vice versa

• sin²θ + cos²θ = 1

• sec²θ - tan²θ = 1

• cosec²θ - cot²θ = 1

Solution :

Given that, sinθ = $\bold{\dfrac{m}{n}}$

Then, cosθ = $\bold{\dfrac{\sqrt{n^{2}-m^{2}}}{n}}$

since cosθ = $\bold{\sqrt{1-sin^{2}\theta}}$

tanθ = $\bold{\dfrac{sin\theta}{cos\theta} = \dfrac{m}{\sqrt{n^{2}-m^{2}}}}$

cotθ = $\bold{\dfrac{1}{tan\theta} = \dfrac{\sqrt{n^{2}-m^{2}}}{m}}$

Now, $\bold{\dfrac{tan\theta+4}{4cot\theta+1}}$

= $\bold{\dfrac{\dfrac{m}{\sqrt{n^{2}-m^{2}}}+4}{4\dfrac{\sqrt{n^{2}-m^{2}}}{m}+1}}$

= $\bold{\dfrac{m+4\sqrt{n^{2}-m^{2}}}{4\sqrt{n^{2}-m^{2}}+m}\times \dfrac{m}{\sqrt{n^{2}-m^{2}}}}$

= $\bold{\dfrac{m}{\sqrt{n^{2}-m^{2}}}}$

⇒ $\boxed{\bold{\dfrac{tan\theta+4}{4cot\theta+1} =\dfrac{m}{\sqrt{n^{2}-m^{2}}}}}$ ,

which is the required value.

Answer 2

bhai yrr follow karo mujhe