If sin theta is 6 by 10 then the value of tan theta +sec theta
Answers
Answer:
Given:-
\sf \sin{ \theta} = \dfrac{6}{10}sinθ=106
To find:-
\sf Value\;of\; \tan{ \theta} + \sec{ \theta}Valueoftanθ+secθ
Solution:-
We have, \sf \sin{ \theta} = \dfrac{6}{10} = \dfrac{3}{5}sinθ=106=53
\sf \sin{ \theta} = \dfrac{3}{5} = \dfrac{Height}{Hypotenuse}sinθ=53=HypotenuseHeight
\star\sf {\underline{Using\;Pythagoras\;Theorem:-}}⋆UsingPythagorasTheorem:−
\dashrightarrow\sf H^2 = B^2 + P^2⇢H2=B2+P2
\dashrightarrow\sf (5)^2 = B^2 + (3)^2⇢(5)2=B2+(3)2

\dashrightarrow\sf B^2 = 25 - 9⇢B2=25−9
\dashrightarrow\sf B^2 = 16⇢B2=16
\dashrightarrow\sf \sqrt{B^2} = \sqrt{16}⇢B2=16
\dashrightarrow\;{\sf{\purple{B = 4}}}⇢B=4

Therefore,
\sf \tan{ \theta} = \dfrac{height}{base} = \dfrac{4}{3}tanθ=baseheight=34
And
\sf \sec{ \theta} = \dfrac{hypotenuse}{base} = \dfrac{5}{4}secθ=basehypotenuse=45
Now,
Add the values of \sf \tan{ \theta} \; and \; \sec{ \theta} :-tanθandsecθ:−
\dashrightarrow\sf \tan{ \theta} + \sec{ \theta}⇢tanθ+secθ
\dashrightarrow\sf \dfrac{4}{3} + \dfrac{5}{4}⇢34+45
\dashrightarrow\sf \dfrac{16 + 15}{12}⇢1216+15
\dashrightarrow\;{\sf{\red{\dfrac{31}{12}}}}⇢1231
\dag\;\sf Hence\;Solved!!†HenceSolved!!