Show that : sin `30^(@)=sqrt((1-cos60^(@))/(2))` – InterviewSolution

InterviewSolution

1.	Show that : sin `30^(@)=sqrt((1-cos60^(@))/(2))`
Answer» `sin x=1` `rArrsin x=sin 90^(@) " " rArr " " x=90^(@)` `rArr(x)/(3)=(90^(@))/(3)=30^(@) " " :." " tan""(x)/(3)=tan30^(@)=(1)/(sqrt(3))`

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`