Home
Class 12
MATHS
In Delta ABC , prove that : sin (...

In ` Delta ABC ` , prove that :
` sin ((B - C)/(3)) = ((b -c)/(a)) cos ((A)/(2))`

Text Solution

Verified by Experts

In `Delta ABC ` ,
` a/(sinA) = b/(sinB)= c/(sin C)" "` (by sine rule)
By equal ratio theorem we can write .
` (a) /(sin A) = (b - c)/(sin B - sinC )`
` rArr (a)/(b-c) = (sin A)/(sin B - sin C)`
` rArr (b - c)/(a) = (sin B sin C)/(sin A)`
`rArr (b-c)/(a) = (2 sin ((B - C)/(2)). cos ((B + C)/(2)))/(sin A)`
` = (2 sin ((B - C)/(2)). cos ((pi - A)/(2)))/(sinA)`
(` because A + B + C = pi ` , sum of all angles of triangle)
` = (2 sin ((B-C)/(2)) . sin ((A)/(2)))/(2 sin ((A)/(2)) . cos ((A)/(2)))`
` rArr (b-c)/(a) = (sin ((B - C)/(2)))/(cos((A)/2))`
` rArr ((b - c)/(a)) . cos ((A)/(2)) = sin ((B - C)/(2)) `
Promotional Banner

Topper's Solved these Questions

  • MARCH 2019

    GURUKUL PUBLICATION - MAHARASHTRA PREVIOUS YEAR PAPERS|Exercise SECTION-D|13 Videos

  • MARCH 2019

    GURUKUL PUBLICATION - MAHARASHTRA PREVIOUS YEAR PAPERS|Exercise SECTION-B|10 Videos

  • MARCH 2018

    GURUKUL PUBLICATION - MAHARASHTRA PREVIOUS YEAR PAPERS|Exercise SECTION - II|20 Videos

  • OCTOBER 2014

    GURUKUL PUBLICATION - MAHARASHTRA PREVIOUS YEAR PAPERS|Exercise SECTION - II|19 Videos

Similar Questions

Explore conceptually related problems

In any triangle ABC prove that: sin((B-C)/(2))=((b-c)/(a))(cos A)/(2)

In any triangle ABC, prove that following: sin((B-C)/(2))=(b-c)/(a)(cos A)/(2)

In any Delta ABC, prove that (sin B)/(sin(B+C))=(b)/(a)

In any Delta ABC, prove that :(b+c)cos((B+C)/(2))=a cos((B-C)/(2))])

In Delta ABC , prove that (b - c)^(2) cos^(2) ((A)/(2)) + (b + c)^(2) sin^(2) ((A)/(2)) = a^(2) .

For any triangle ABC, prove that (sin(B-C))/(2)=(b-c)/(a)((cos A)/(2))])

In any Delta ABC, prove that: (sin B)/(sin C)=(c-a cos B)/(b-a cos C)

In any Delta ABC ,prove that (sin B)/(sin C)=(c-a cos B)/(b-a cos C)

In a Delta ABC prove that cos((A+B)/(2))])=(sin C)/(2)

In any Delta ABC, prove that :(a-b)/(c)=(sin((A-B)/(2)))/(cos((c)/(2)))