Question

If 4 tan theta-3=0 then find : (1)cosec theta (2)cos theta + sec theta

Answer 1

theta is written as A,

Given, 4 tanA - 3 = 0

4 tanA = 3

tanA = 3/4

Now,

tanA = 3/4

height / base = 3 / 4

Let height = 3x and base = 4x

By Pythagoras Theorem,

( 3x )^2 + ( 4x )^2 = hypotenuse^2

25x^2 = hypotenuse^2

5x = hypotenuse

Hence,

( i ) : cosecA = hypotenuse / height

= 5x / 3x

= 5 / 3

( ii ) :

cosA + secA

=> base / hypotenuse + hypotenuse / base

=> 4x / 5x + 5x / 4x

=> 4 / 5 + 5 / 4

=> ( 16 + 25 )/20

=> 41/20