Question

In a right triangle Sin (40-x)=cos(3x) what is the value of x

Answer 1

Answer:

Value of 'x' = 25

Explanation:

Given in a right triangle ,

sin(40-x)=cos(3x)

$\boxed {sin(90-\theta) = cos\theta}$

Now ,

=> sin(40-x)=sin(90-3x)

=> 40-x=90-3x

Add " 3x " both sides of the equation, we get

=> 40-x+3x=90-3x+3x

=> 40+2x=90

Subtract 40 both sides of the equation, we get

=> 40-40+2x=90-40

=> 2x=50

Divide both sides by (2) , we get

=> x = 25

Therefore,

x = 25

••••

Answer 2

Answer:

The value of x is 25.

Step-by-step explanation:

Right angle triangle is one which one of the angle must be 90 degree.

sin (40-x)= cos (3x)                      

sin(40-x)= sin (90-3x) because the trigonometry identity: cosθ= sin (90-θ)        

sin on both the sides gets cancelled, therefore

40-x= 90-3x

3x-x=90-40                    

Subtracting the like terms on right hand side and left hand side,

2x = 50

Taking 2 on right hand side,

x= 50/2

x=25

Therefore, the value of x is 25.