sin^2(x) + cos(x) = 2

Question

shubhamsrg · Answer

sin^2(x) =1-cos^2(x) ..it now forms a quadratic in cos x ..

anonymous · Answer

attachment

anonymous · Answer

I know it becomes (1-cos^2(x)) + cos(x) = 2.

anonymous · Answer

But I don't know how to solve for x value. The answer should be in degrees or radians.

callisto · Answer

Not sure if it is correct
sin^2(x) + cos(x) = 2
(1-cos^2(x)) + cosx -2=0
cos^2x - cosx +1 =0
=> no real solution...

shubhamsrg · Answer

well it becomes cos^2(x) - cos x + 1 = 0 ..
aha..i see..it gives a complex solution..

saifoo.khan · Answer

-cos^2x + cos x -1 = 0

For problems like these,
suppose cos^x = z

-z^2 + z -1 = 0
And solve the quadratic.

shubhamsrg · Answer

the complex solution is not very tough to get here but i guess its of no use here..hmmn..

apoorvk · Answer

@Callisto you made a 'silly-mistake' in your equation.

callisto · Answer

Please point it out.
It's the nth times I made silly mistakes today. Sorry

apoorvk · Answer

(1-cos^2(x)) + cosx -2=0
this simplifies to--> -cos^2(x) + cosx -1 = 0

You were doing perfectly otherwise, don't worry.

callisto · Answer

Divided both sides by -1, wouldn't it be cos^2x - cosx +1 =0?