If `sintheta + 2 costheta=1`,then prove that `2sintheta-costheta=2`. – InterviewSolution

InterviewSolution

1.	If `sintheta + 2 costheta=1`,then prove that `2sintheta-costheta=2`.
Answer» Given, `sintheta+2costheta=1` On squaring both sides, we get `(sintheta+2costheta)^(2)=1` `sin^(2)theta+4cos^(2)theta+4sintheta.costheta=1` `rArr (1-cos^(2)theta) + 4(1-sin^(2)theta)+4sintheta.costheta=1` `[therefore sin^(2)theta+ cos^(2)theta=1]` `rArr 4sin^(2)theta + cos^(2)theta-4sintheta. costheta=4` `rArr (2sintheta-costheta)^(2)=4` `[therefore a^(2)+b^(2)-2ab=(a-b)^(2)]` `rArr 2sintheta-costheta=2` Hence proved.

Discussion

No Comment Found

Related InterviewSolutions

If A, B and C are interior angles of a triangle ABC, then show that `sin((B+C)/2)=cos(A/2)`.
If A, B and C are interior angles of a triangle ABC, then show that `sin((B+C)/2)=cosA/2`.
Prove that : `(sinalpha+cosalpha)(tanalpha+cotalpha)=secalpha+"cosecα"`.
Given `sec theta=(13)/(12)`, calculate all other trigonometric ratios.
Evaluate : `cos60^(@)cos30^(@)+ sin 60^(@)sin30^(@)`
Show that : sin `30^(@)=sqrt((1-cos60^(@))/(2))`
given that `tan(theta_1 + theta_2) = (tantheta_1 + tantheta_2)/(1-tantheta_1*tantheta_2)` find `(theta_1+theta_2)` when `tantheta_1 =1/2 , tantheta_2=1/3`
If `asintheta+bcostheta=c` then prove that `acostheta-bsintheta=sqrt(a^2+b^2-c^2)`
Shown that : `tan48^(@)tan23^(@)tan42^(@)tan67^(@)=1`
Express `cot 85^o +cos75^o`in terms of trigonometric ratios of angles between `0^o`and `45^o`