Question

if 4sin theeta + 3sin theeta =5,find the value of tan theeta

Answer 1

let theeta = x
4sinx+ 3sinx= 5
7sinx=5
sinx=5/7

so, cosx= √1- sin^2x=√1-(5/7)^2=√1-25/49
=√24/49=(2√6)/7

so, tanx= sinx/ cosx
= (5/7)/2√6/7
=5/2√6

Hope it is useful

Answer 2

4 sin theta + 3 sin theta = 5

=> 7 sin theta = 5

=> sin theta = 5 /7

=> P / H = 5 /7


Let the Perpendicular be 5a

Hypotenuse = 7a

Now,

Base^2 + Perpendicular^2 = Hypotenuse^2

=> Base^2 + (5a)^2 = (7a)^2

=> Base^2 = 49a^2 - 25a^2

=> Base^2 = 24a^2

$= > base \: = 2\sqrt{6} a$


Now,

$\tan \: theta \: = \frac{5a}{2 \sqrt{6}a } \\ \\ = \frac{5}{2 \sqrt{6} } \\ \\ = \frac{5 \sqrt{6} }{12}$