Question

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


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Answer 1

$\huge{\boxed{\tt{Answer:-}}}$

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

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

$\huge{\boxed{\tt{Explanation:-}}}$

According to trigonometry identity cosθ= sin (90-θ)

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

(sin on both the sides gets cancelled)

Therefore:-

40-x= 90-3x

3x-x=90-40

Subtracting the like terms on RHS and LHS,

2x = 50

Taking 2 on right hand side,

x= 50/2

$\large{\boxed{\tt{x=25}}}$

Therefore, the value of x is 25.

Answer 2

sin( 40 - x) = cos3x

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

=>50 + x = 3x

=>2x = 50

=>x = 25

formula used

sin( 90 - a) = cosa