Question

if Tantheta=3/4 find sintheta, costhta, Tantheta+cottheta​

Answer 1

Given :-

• Tan$\theta$ = $\frac{3}{4}$

We know that

• Tan$\theta$ = $\frac{Perpendicular}{Base}$

Let , Perpendicular = 3x

• Base = 4x

By hypotenuse :-

$= > \sqrt{( {3x})^{2} \: + \: ( {4x})^{2} }$

$= > \sqrt{ {9x}^{2} \: + \: {16x}^{2} }$

$= > \sqrt{ {25x}^{2} }$

$= = = > 5x$

We know that

$\rightarrow$ Sin$\theta$ = $\frac{ Perpendicular}{Hypotenuse}$

• $\frac{3x}{5x}$

:. Sin $\theta$ = $\frac{3}{5}$ ✔️

Similarly,

$\rightarrow$ Cos$\theta$ = $\frac{ Base}{Hypotenuse}$

• $\frac{4x}{5x}$

:. Cos $\theta$ = $\frac{4}{5}$✔️

As we know that

$\rightarrow$ Cot $\theta$ is the reciprocal of Tan $\theta$

:. Cot $\theta$ = $\frac{ 4}{3}$ ✔️

$\rightarrow$ Tan $\theta$ + Cot $\theta$

$\rightarrow$ $\frac{3}{4}$ + $\frac{4}{3}$

$\rightarrow$ $\frac{ (3×3) \: + \: (4×4)}{(4 \: × \: 3)}$

$\rightarrow$ $\frac{(9 \: + \: 16)}{12}$

$\rightarrow$ $\frac{25}{12}$

:. Tan$\theta$ + Cot$\theta$ = $\frac{25}{12}$✔️