Question

1) If cos theta= 9/15,then find tan theta,sec theta and sin theta.

2)If cosec theta = 17/8, then find sin theta and cos theta.​

Answer 1

Answer:

solve both question in photo

Answer 2

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\mathtt{\huge{\underline{\red{Answer\: :}}}}$

$\: \bigstar \green{ \bold{ \underline{ \underline{step \: by \:step \: explaination: }}}}$

$\pink{Given}=\begin{cases} cos\theta=\dfrac{9}{15} \\ \\ tan\theta=? \\ \\ \sec\theta=? \\ \sin\theta =?\end{cases}$

$\: \\ \quad \implies \displaystyle \sf{ cos \theta = \frac{adjacent \: side}{hypothenuse} } = \frac{9}{15}$

$\: \: \bullet \underline{ \bf{ \: by \: using \: pythagoras \: theorem}}$

$\quad\implies\displaystyle\sf{(AC)^2=(AB)^2+(BC)^2}$

$\quad\implies\displaystyle\sf{(15)^2=(9)^2+(BC) ^2}$

$\quad\implies\displaystyle\sf{225-81=(BC)^2}$

$\quad\implies\displaystyle\sf{BC=\sqrt{144}}$

$\quad\implies\boxed{\underline{\displaystyle\sf{BC=12cm}}}$

$\: \implies \displaystyle \sf{tan \theta = \frac{opposite side}{adjacent \: side} = \frac{12}{9}}$

$\: \: \implies \displaystyle \sf{sec \theta = \frac{1}{cos \theta} = \frac{1}{ \frac{9}{15} } = \frac{15}{9} }$

$\: \\ \ \: \implies \displaystyle \sf{sin \theta = \frac{opposite \: side}{hypothenuse} = \frac{12}{15} }$

$\pink{▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬}$

$\green{Given}=\begin{cases} cosec\theta=\dfrac{17}{8} \\ \\ sin\theta=? \\ \\ cos\theta=? \end{cases}$

$\: \: \\ \implies \displaystyle \sf{cosec \theta = \frac{1}{ sin \theta } } = \frac{1}{ \frac{opposite \: side}{hypothenuse} }$

$\: \: \implies \displaystyle \sf{sin \theta = \frac{1}{ \frac{17}{8} } = \frac{8}{17} }$

$\: \: \bullet \displaystyle \bf{hypothenuse = 17}$

$\: \bullet \displaystyle \bf{opposite \: side} = 8$

$\: \: \bigstar \underline{\bf{by \: using \: pythagoras \: theorem}}$

$\implies\displaystyle\sf{(AC)^2=(BC)^2+(AB)^2}$

$\implies\displaystyle\sf{(17)^2=(8)^2+(AB)^2}$

$\implies\displaystyle\sf{289-64=(AB)^2}$

$\implies\displaystyle\sf{225=(AB)^2}$

$\implies\displaystyle\sf{AB=15cm}$

$\: \: \implies \displaystyle \sf{ab = cos \theta}$

$\: \: \\ \implies \displaystyle \sf{cos \theta = \frac{adjacent \: side}{hypothenuse} = \frac{15}{17} }$

$\red{▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬}$