Home > Trigonometry > Solving Trigonometric Equations

How do you solve #sin(60-x)=2sinx#?

Answer 1

Dylan Arnold

Use the trig identity: #sin (a - b) = sin a.cos b - sin b.cos a#

#sin (60 - x) = sin 60.cos x - cos 60.sin x = (sqr3/2).cos x - (sin x)/2#

(sqr3).cos x - sin x = 4.sin x#

#f(x) = (sqr3).cos x - 5sin x = 0.# Divide by cos x -->

#(Condition: cos x not 0 -> x not pi/2 and x not 3pi/2)#

#f(x) = sqr3 - 5tan x -> tan x = (sqr3)/5 = 0.35#

Calculator gives #x = 19.10 + k.pi#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Oliver Atkinson

To solve the equation sin(60-x) = 2sin(x), you first apply the angle subtraction formula for sine, which states sin(A - B) = sinAcosB - cosAsinB. Then, you simplify the equation and solve for x. After some algebraic manipulation, the solution for x is x = 30°.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.