Solve Trigonometric equation:- sinx +cosx +sin2x=1/2.............reply fast....

Question

Solve Trigonometric equation:-  sinx +cosx +sin2x=1/2.............reply fast....

anonymous · Answer

sin2x can be rewritten

anonymous · Answer

ya as 2sinxcosx but what next?

shubhamsrg · Answer

2sinx + 2cos x + 4sinx cosx = 1
2sinx( 1 + 2cosx) + 2cosx = 1
2sinx(1+ 2cosx) + (1+2 cosx) =2

(1+ 2sinx)(1+2cosx) = 2

shubhamsrg · Answer

I don't have much idea next, leme see

anonymous · Answer

yes thanks a lot thats absolutely fine! i got an idea to solve the question

shubhamsrg · Answer

Will you share that idea ?

anonymous · Answer

2sinx=1; 2cosx=1 and further by the formulae sin theta =sin alpha and so on....

shubhamsrg · Answer

sinx and cosx both can not be 1/2 for the same value of x, you're logic is flawed.

shubhamsrg · Answer

Its quite complicated to solve this, are you sure you have the right ques ?

anonymous · Answer

i know there may be some problem in the question or the expansion....wait..question is cosx+sinx-sin2x=1/2 so in that way it can be solved

shubhamsrg · Answer

-sin2x !!

shubhamsrg · Answer

its easily solvable then

shubhamsrg · Answer

2cosx + 2sinx - 4sinx cosx = 1

2sinx(1 - 2cosx) = (1-2cosx)
=>(2sinx)(1- 2cosx) =0

BAZINGA !

anonymous · Answer

wow!!! thanks....i was a bit confused....thanks a lot!

shubhamsrg · Answer

Glad to have helped.

shubhamsrg · Answer

Correction :

shubhamsrg · Answer

it'll be
(1-2sinx)(1- 2cosx) =0

anonymous · Answer

ya i got that....k thanks bye gtg