## leenajain.1996 2 years ago Solve Trigonometric equation:- sinx +cosx +sin2x=1/2.............reply fast....

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1. SmartWish

sin2x can be rewritten

2. leenajain.1996

ya as 2sinxcosx but what next?

3. shubhamsrg

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

4. shubhamsrg

I don't have much idea next, leme see

5. leenajain.1996

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

6. shubhamsrg

Will you share that idea ?

7. leenajain.1996

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

8. shubhamsrg

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

9. shubhamsrg

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

10. leenajain.1996

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

11. shubhamsrg

-sin2x !!

12. shubhamsrg

its easily solvable then

13. shubhamsrg

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

14. leenajain.1996

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

15. shubhamsrg

Glad to have helped.

16. shubhamsrg

Correction :

17. shubhamsrg

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

18. leenajain.1996

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