Question

if cos theta =12\13,find the value of cot theta + cosec theta​

Answer 1

$\star \; {\underline{\boxed{\pmb{\orange{\frak{ \; Given \; :- }}}}}}$

• $\sf{ Cos \; \theta = \dfrac{12}{13} }$

$\star \; {\underline{\boxed{\pmb{\purple{\frak{ \; To \; Find \; :- }}}}}}$

• $\sf{ Cot \; \theta + CoSec \; \theta }$

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$\star \; {\underline{\boxed{\pmb{\red{\frak{ \; SolutioN \; :- }}}}}}$

❍ Deriving the Value of θ :

• $\purple{\pmb{\sf{ Cos \; \theta = \dfrac{Base}{Hypotenuse} }}}$

So, We Have :

$\begin{gathered} \; \; \longrightarrow \; \; \sf{ Cos \; \theta = \dfrac{Base}{Hypotenuse} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \longrightarrow \; \; {\underline{\boxed{\pmb{\sf{ Cos \; \theta = \dfrac{12}{13} }}}}} \; {\green{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

❍ Deriving the Base :

$\begin{gathered} \; \; \implies \; \; \sf{ Base = \sqrt{ \bigg( Hypotenuse \bigg)^{2} - \bigg( Perpendicular \bigg)^{2} } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \implies \; \; \sf{ Base = \sqrt{ \bigg( 13 \bigg)^{2} - \bigg( 12 \bigg)^{2} } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \implies \; \; \sf{ Base = \sqrt{ 169 - 144 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \implies \; \; \sf{ Base = \sqrt{ 25 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \implies \; \; {\underline{\boxed{\pmb{\sf{ Base = 5 }}}}} \; {\red{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

❍ Calculating the Value of given Equation :

• $\pink{\pmb{\sf{ Cot \; \theta = \dfrac{Base}{Perpendicular} }}}$

• $\red{\pmb{\sf{ Cosec \; \theta = \dfrac{Hypotenuse}{Perpendicular} }}}$

So, We Have :

$\begin{gathered} \; \; \dashrightarrow \; \; \sf{ Cot \; \theta + Cosec \; \theta } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \dashrightarrow \; \; \sf{ \dfrac{Base}{Perpendicular} + \dfrac{Hypothese}{Perpendicular} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \dashrightarrow \; \; \sf{ \dfrac{5}{12} + \dfrac{13}{12} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \dashrightarrow \; \; \sf{ \dfrac{5 + 13}{12} }\\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \dashrightarrow \; \; \sf{ \dfrac{18}{12} }\\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \dashrightarrow \; \; \sf{ \cancel\dfrac{18}{12} }\\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \dashrightarrow \; \; {\underline{\boxed{\pmb{\sf{ \dfrac{3}{2} }}}}} \; {\orange{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

❍ Therefore :

$\qquad \; {\red{\bigstar}} \; {\underline{\overline{\boxed{\purple{\pmb{\sf{ Cot \; \theta + Cosec \; \theta = \dfrac{3}{2} }}}}}}} \; {\red{\bigstar}}$

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:)

Answer 2

Answer:

Hey learner here is your answer :--

5 is the answer

Step-by-step explanation:

Given :--

Cos theta = 12/13

Required to find:--

The value of cot theta + cosec theta

Solution:--

→ Cos theta = 12/13 ,

cos theta = base/hypotenuse

→ we have to find the perpendicular to find out the other trigonometric angles

→ as we know that by using Pythagoras theorem we can conclude that

(Hypotenuse)² = (Base)²+(Perpendicular)²

→ (perpendicular) =√(Hypotenuse)²- (Base)²

→ P = √169-144

→ P = √25

→ P = 5

Now,

cot theta + cosec theta

$\frac{12}{5} + \frac{13}{5}$

$\frac{25}{5}$

$5$