Home
Class 12
MATHS
Prove that: (sin(B-C))/(cosBcosC)+(sin(C...

Prove that: `(sin(B-C))/(cosBcosC)+(sin(C-A))/(cosCcosA)+(sin(A-B))/(cosAcosB)=0`

Text Solution

Verified by Experts

The first term of the LHS is
`(sin(B-C))/(cos B cos C)=(sin B cos C-cos B sin C)/(cos B cos C)`
`=(sin B cos C)/(cos B cos C)-(cos B sin C)/(cos B cos C)=tan B-tan C`
Similarly, the second term of the LHS is `(tan C-tan A)` and the third term of the LHS is `(tan A-tan B)`
Now LHS`=(tan B-tan C)+(tan C-tan A)`
`+(tan A-tan B)=0`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.1|11 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.2|7 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

Prove that (a^2sin(B-C))/(sinb+sinC)+(b^2"sin"(C-A))/(sinC+sinA)+(c^2"sin"(A-B))/(sinA+sinB)=0

In any triangle ABC prove that (a^(2)sin(B-C))/(sinA)+(b^(2)sin(C-A))/(sinB)+(c^(2)sin(A-B))/(sinC)=0

(sin(A - B))/(cos A cos B) + (sin (B - C))/( cos B cos C) + (sin(C - A))/(cos C cos A) is

Prove that (sin (A-B))/(sin (A+B))=(a^(2)-b^(2))/(c^(2))

Prove that sin (A+B)= sin A cos B + cos A sin B.

Show that suma sin(B-C) =0

In a Delta ABC, prove that (a sin(B - C))/(b^(2) - c^(2)) = (b sin (C - A))/(c^(2) - a^(2)) = (c sin (A - B))/(a^(2) - b^(2))

Prove that sin (A+B) sin (A-B)=cos^(2) B-cos^(2) A

Show that cos[(B-C)/2]=(b+c)/a sin(A/2)