Thread: Trigonometric equation

Can someone please help me solve the following trig equations please? Thanks

1-tan^2(x)/1+tan^2(x) + cos(x) = 0

(sqrt(3)+1)cos^2(x) - 1 = (sqrt(3)-1)sin(x)cos(x)

Thanks heaps

Originally Posted by deltaxray

Can someone please help me solve the following trig equations please? Thanks

1-tan^2(x)/1+tan^2(x) + cos(x) = 0

(sqrt(3)+1)cos^2(x) - 1 = (sqrt(3)-1)sin(x)cos(x)

Thanks heaps

Hi

Did u mean solve the trigonometric equation ? If so ,

For (1) ,







Then , i think you should be able to continue from here .

Thanks Mate.

Hello deltaxray

Welcome to Math Help Forum!

Originally Posted by deltaxray

Can someone please help me solve the following trig equations please? Thanks

1-tan^2(x)/1+tan^2(x) + cos(x) = 0

(sqrt(3)+1)cos^2(x) - 1 = (sqrt(3)-1)sin(x)cos(x)

Thanks heaps

For question 2, divide both sides by :



Then express everything in terms of . Re-arrange as a quadratic in , and you'll find it factorises into:



Can you fill in the gaps?

Grandad

Thanks granddad. I got it

by inspection, pi is a root to the equation, the other 2 roots are found already; x = {pi/3, pi, 5pi/3}

the graph below confirms it