Question

if cosec theta is equal to 5 by 3 then what is the value of cos theta + 10 theta

Answer 1

Theta us written as A,

Given, cosecA = 5 / 3



We Know, cosec∅ = hypotenuse / height

Hence, 5 / 3 = hypotenuse / height



So, let hypotenuse = ( 5x ) and height be ( 3x )


By Pythagoras theorem, base will be ( 4x )



Hence,
cosA = base / hypotenuse

cosA = 4x / 5x

cosA = 4 / 5



tanA = height / base

tanA = 3x / 4x

tanA = 3 / 4





Then, cosA + tanA


=> 4 / 5 + 3 / 4

=> ( 16 + 15 ) /20

=> 31 / 20





$.$

Answer 2

Heya !!




Cosec theta = 5/3 = H/P




H = 5 and P = 3





By Pythagoras theorem,



( H )² = (B)² + (P)²



( B)² = (H)² - (P)²




( B)² = (5)² - (3)² = 25 - 9



B = root 16 = 4





Therefore,



Cos theta = B/H = 4/5


And,



Tan theta = P/B = 3/4









----------------------------



Cos theta + Tan theta


=> 4/5 + 3/4





=> ( 16 + 15 / 20 )



=> 31/20